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AbstractIn graph theory, a graph is a mathematical structure that consists of a set of vertices and a set of edges connecting those pairs of vertices. Let G=(V,E) be a graph, a dominating set for G is a subset D⊆V of vertices such that every vertex in V∖D has at least one neighbor in D. The domination number of G, denoted by γ(G), is the minimum cardinality of a dominating set in G. Recently, Khan (2023) performed a comparative study of seven important domination parameters with the π-electronic energy of benzenoid hydrocarbons, with a new theoretical approach. Physico-chemical properties are crucial for understanding the physical and chemical behavior of a molecule. In this paper, we perform a comparative study of those seven domination parameters with the physico-chemical properties of benzenoid hydrocarbons. We find the values of those domination parameters for the 22 lower benzenoid hydrocarbons and follow the statistical approach described by Khan (2023). The two physico-chemical properties to be chosen are the normal boiling point Tb, a representative for intermolecular and van-der-Waals type interactions, whereas, the standard enthalpy/heat of formation ΔHfo is referred to represent the thermal properties of a molecular graph. This study further enhances that the performance of paired domination number is exceptional among all other parameters and highly correlated with both of the physico-chemical properties. Its correlation coefficient is 0.9981 (respectively, 0.9726) with Tb (respectively, ΔHfo). The outstanding correlation coefficient of paired domination number ensures further usage in quantitative structure-property relationship (QSPR) models. [ABSTRACT FROM AUTHOR]

Let S be a groupoid (magma) with zero 0, and let R = ⊕ s ∈ S R s be a contracted S-graded ring, that is, an S-graded ring with R 0 = 0. By G (H R) we denote the undirected power graph of a multiplicative subsemigroup H R = ∪ s ∈ S R s of R, and by G * (H R) a graph obtained from G (H R) by removing 0 and its incident edges. If Re is a nonzero ring component of R, then G * (R e) denotes a subgraph of G * (H R) , induced by R e *. In this paper we address a problem raised in [Abawajy, J., Kelarev, A., Chowdhury, M.: Power Graphs: A Survey. Electron. J. Graph Theory Appl. 1(2), 125–147 (2013)]. Namely, let S be torsion-free, that is, s n = t n implies s = t for all s, t ∈ S , and all positive integers n, and let S be 0-cancellative, that is, for all s, t, u ∈ S , su = tu ≠ 0 implies s = t , and us = ut ≠ 0 implies s = t. Also, let R be semisimple Artinian. We prove that if G * (R e) is connected for every nonzero ring component Re of R, then the connected components of G * (H R) are precisely the graphs G * (R e). [ABSTRACT FROM AUTHOR]

Topological indices have gained significant attention in the field of chemical graph theory. These indices offer quantitative measures that accurately represent the topology of molecular graphs, which are used to model chemical compounds. Generally, their physical properties are closely linked to the geometric structures of these compounds. In this paper, we introduce a new family of phenylene-quadrilateral networks that exhibit unique features. These studied topological structures can be seen as generalizations of the phenylenes. To analyze the generalized phenylene-quadrilateral networks, we propose a recursive method for calculating their Kirchhoff index and the number of spanning trees. This method is based on the relationship between the coefficients and roots of the characteristic polynomial. [ABSTRACT FROM AUTHOR]

A topological index is a number used in QSAR and QSPR research to assess the structural properties of a graph. The Sadhana and PI, polynomial-based topological indices, have been intensively explored in the study of chemical graph theory since a few years ago. These indices are computed using their related polynomials, however, in this study, we use an instantaneous and revolutionary approach to compute these indices for hexagonal boron nitride graphs and carbon nanotube structures. [ABSTRACT FROM AUTHOR]

This paper studies the exponential bipartite synchronisation in mean square (EBS-MS) of stochastic signed networks (SSNs) via periodically intermittent pinning control. It is important to note that intermittent control is an extension of existing literature, which depends on discrete observations instead of continuous observations during the work period. Additionally, only a small percentage of the network nodes are controlled by intermittent control. Several sufficient conditions are established by the Lyapunov method and graph theory. Especially, when the duration τ between two consecutive observations tends to zero, our control will degenerate into common periodically intermittent pinning control. Meanwhile, a corollary about the EBS-MS of SSNs is presented. Besides, theoretical results are applied to a single-link robot arm system and an oscillator system. Finally, numerical simulations are presented to show the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

Hydrodynamic models are used to analyse water networks (water distribution, drainage, surface water, district heating, etc.). The non-linear nature of water flows necessitates the use of iterative solution methods in hydraulic modelling. This requires a relatively large computational effort. To reduce this effort, networks, network forcing and/or the flow in networks are often simplified and analysed using the Graph Theory. The simplification options depend on the network characteristics. There are many topological features to describe Graph-based networks. In this paper, these characteristics are summarised, applied on 7 urban drainage networks and discussed. As the topological features do not describe the networks in a uniform manner, a new type of topological characterisation of looped drainage networks (Network Linearisation Parameter, NLP) is proposed based on linearized hydraulics and bottlenecks identified in paths to outfalls. [ABSTRACT FROM AUTHOR]

AbstractMolecular descriptors are essential tools that bridge the gap between chemical structures and their properties. Among these, the Randić index (R), geometric-arithmetic index (GA), and arithmetic-geometric index (AG) are well-established. However, the relationships between these descriptors, particularly the gaps GA−R and AG−R, have not been extensively explored. This study investigates the impact of these descriptor gaps on chemical graph theory. Our findings reveal that the differences GA−R and AG−R provide unique insights into the structure-property modeling of molecules, particularly outperforming AG, GA, R, and other known descriptors for alkanes. Polycyclic aromatic compounds (PACs) are organic molecules composed of multiple fused aromatic rings. PACs are of significant environmental concern due to their persistence and potential toxicity, including carcinogenic properties. The effectiveness of GA−R and AG−R is observed to be strong in structure-property modeling for some polycyclic aromatic compounds. Additionally, GA−R and AG−R are recognized as important descriptors for various pharmaceutical compounds employed in treating malignant diseases. [ABSTRACT FROM AUTHOR]

Theoretical, methodological, and empirical contributions regarding networks within the context of graph theory constitute a valuable interface between geography and mathematics. Seeking to assess mathematical network geography's past, present, and future, this article addresses such research and literature by discussing new knowledge produced from networked geographic phenomena—especially Erdös collaboration graphs depicting mentorships or authorships among scholars; outlining a brief history of networks in geographical analysis; and couching spatial autocorrelation within its geographic network links. General commentary transitions into examples of Erdös graphs and their implications for collaborations. The narrative also speaks to networked space challenges of established geographic thought (e.g., Tobler's first law of geography), with special reference to contributions by Boots and his coauthors. This article concludes with a treatment of graph theory, networks, and spatial autocorrelation. [ABSTRACT FROM AUTHOR]

As industrial Internet of things (IIoT) for Manufacturing Service Collaboration (MSC) is becoming the current trend to accelerate the upgrade iteration of manufacturing capability, developing the robust IIoT platform operation mechanism for MSC is crucial to promote the continuous and stable service collaboration in the presence of supply and demand uncertainties. This paper studies the operational robustness of the IIoT platform for MSC. Firstly, the operation performances, requirements, and challenges of the IIoT platform towards manufacturing collaboration are analysed in classified platform practices, which can provide a comprehensive cognition about platform operation for manufacturing collaboration. Then, to evaluate the tolerance and persistence capabilities of MSC under supply and demand uncertainties, a graph-based operational robustness analysis method of the IIoT platform for MSC is proposed. The IIoT platform operation network for MSC is modelled as an interdependent network-of-network structure based on graph theory, which helps to characterise MSC performance properties under complexities. By combining manufacturing properties with network statistics, the evaluation metrics of operational robustness are established, which is done to quantise the MSC effectiveness under uncertainty effects. A case about customised manufacturing of automobiles illustrates the application of the proposed methods. Finally, future studies about robust MSC regulation are discussed. [ABSTRACT FROM AUTHOR]

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with graphs. We have thus analysed them adapting the methodology for computing the degrees of acquisition of the Van Hiele levels. Our analysis leads to different proof profiles of Graph Theory students whose characteristics provide empirical support to consider proof levels in Graph Theory from the perspective of the Van Hiele model. [ABSTRACT FROM AUTHOR]

Aiming at the mutual coupling of multiple physical fields in the microwave heating process and the generation of thermal runaway phenomenon, in this paper, a cooperative variable power heating strategy with multi-microwave source clusters under dynamic switching topology is proposed in order to improve the temperature uniformity. Firstly, an algebraic graph theory is used to establish a communication topology for complete information transfer, which is used to construct a distributed structure among multiple microwave source intelligences. Secondly, the dynamic topology switching algorithm under event triggering is introduced, and the real-time temperature distribution of the heated materials is considered to achieve the dynamic switching of the topology connection mode between microwave source clusters in order to synchronously coordinate the power consistency output between different clusters. On this basis, a numerical calculation model is constructed to solve the mixed optimization of integer and continuum variables by means of the finite element method. Finally, the effectiveness of the heating strategy to improve temperature uniformity is verified by microwave heating SiC media simulation calculation. The numerical calculation results show that the temperature uniformity indexes are improved by 34.1%–50.4% and 28.1%–55.2% in each horizontal and vertical section for single materials, and by 59.1%–59.7% and 46.5%–63.4% in each horizontal and vertical section for multi-materials, respectively, in comparison with the general heating method. This strategy effectively avoids the residence of hot and cold spots in the material, which in turn optimizes the temperature distribution. [ABSTRACT FROM AUTHOR]

This paper proposes a novel method that integrates a tailored spectral graph metric and economic aspects within a coupled bi-objective optimization framework for the simultaneous pipe sizing and partitioning of water distribution networks (WDNs). Besides minimum pressure head and topological WDN connectivity, the telescopic diameter distribution criterion is applied through a new algorithm in the sizing phase to help the optimization converge towards sound engineering solutions. The application of the proposed method to a synthetic layout and a real Italian case study proves the superiority of the solutions obtained with the novel method from hydraulic and managerial/operational viewpoints in comparison with those obtained with a traditional decoupled method (separate pipe sizing and partitioning) in terms of i) compliance with service pressure constraints and ii) ease of management following WDN partitioning into district metered areas (DMAs). [ABSTRACT FROM AUTHOR]

The authors present a Web application they designed in the R programming language as an experiential learning tool for teaching production theory. The app simulates production decisions where a manager is tasked to find the optimal mixture of inputs through experimentation. Users of the application are instructed to use calculations and intuitions from production theory to improve profitability quickly. The underlying parameters and starting points are randomized to allow for additional practice. Variations of the exercise correspond to cost-minimization and profit-maximization problems with and without market power in the output market. Also, the app provides dynamic, interactive visualizations in 3D in order to assist in a better understanding of standard production theory graphs. The app is located at . [ABSTRACT FROM AUTHOR]

Spectral clustering, as an algorithm based on graph theory and spectral theory, has shown excellent performance in the classification tasks of hyperspectral images in recent years. Although better results have been achieved, some challenges still exist. The inclusion of a priori information can increase the performance of spectral clustering algorithms; however, in practice, it is often unable to meet the demand for a priori information; at the same time, spectral clustering for the quality of the similarity matrix is demanding, and some of the current algorithms are to improve the similarity matrix from the aspect of data planning, and ultimately for the label feature matrices are diluted. In response to the above problems, this paper proposes a self-supervised spectral clustering with spectral embedding (SESSC). The algorithm obtains a low-dimensional representation of the data through spectral embedding, which can simplify clustering while preserving feature information; then uses the similarity matrix about the data and the guidance of the sample constraint information to obtain a new similarity matrix in order to further refine the structural graph, and the result can feed back and optimize the label feature matrix and the low-dimensional representation of the data. Additionally, we introduce a fractional theory in the update of the sample variable matrix, which assures the integrity and validity of the information in the update. Experimental results show that the proposed algorithm has better performance in hyperspectral image classification than existing spectral clustering algorithms. [ABSTRACT FROM AUTHOR]

The ranking of nodes in a network according to their centrality or ''importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The COVID-19 pandemic has recently rejuvenated the interest in this problem, as the ranking may be used to decide who should be tested, or vaccinated, first, in a population of asymptomatic individuals. In this paper, we review classic methods for node ranking and compare their performance in a benchmark network that considers the community-based structure of society. The outcome of the ranking procedure is then used to decide which individuals should be tested, and possibly quarantined, first. Finally, we also review the extension of these ranking methods to weighted graphs and explore the importance of weights in a contact network by providing a toy model and comparing node rankings for this case in the context of disease spread. [ABSTRACT FROM AUTHOR]

This study investigates a new hybrid algorithm, which is a combination of an enhanced elephant herding algorithm (EEHA) and the Jaya algorithm (JA). This hybrid enhanced elephant herding jaya algorithm (EEHJA) controls the searching properly from global exploration to local exploitation to obtain a near-global optimum. The suggested algorithm is employed to optimise the reconfiguration and integration of renewable distributed generations (DGs) taking the novel type of buses P, PQV. The voltage at the PQV bus is regulated by the P bus with a reactive power assist (RPA). Sensitivity factors based on curtailment in active power loss (APL) and enhancement in bus voltages are proposed to obtain optimal DG locations. During reconfiguring network topology (RNT), a smart graph theory technique based on the spanning tree concept authenticates the topological restrictions. The proposed algorithm is applied to optimise the RPA at the P bus, solar photovoltaic DGs ratings, and optimal RNT of the power distribution system (PDS) to minimise the APL. The placement of solar photovoltaic DGs has been studied in two approaches namely, sequential and non-sequential allotment. Further, different cases are studied based on optimum RNT including and excluding DGs, and RPA by the suggested methodology on 33 and 69 bus radial PDS. Moreover, the pollutant emissions like CO2, SO2, and NOX in the environment due to traditional energy sources are further reduced. The adequacy of this novel methodology is verified with recently developed meta-heuristic algorithms and the obtained numerical results demonstrate the validity and its effectiveness. [ABSTRACT FROM AUTHOR]

Multiple kernel learning (MKL) is an efficient way to improve hyperspectral image classification with few training samples by integrating spectral and spatial features. Nonetheless, presenting a MKL algorithm to capture significant information and eliminate redundancy is indispensable. In this paper, a novel graph-based MKL method (GMKL) is introduced to enhance the performance of the MKL algorithm and achieve high discriminative features, resulting in maximum separability. To do so, an informative low-rank graph is determined via a new algorithm called block diagonal representation that takes into account both local and global data structures. Then, in lieu of a time-consuming search for finding the optimal combination of the basic kernels, unlike the prior works, an optimal projective direction is acquired using graph theory. Various basic kernels generated from superpixels and attribute profiles are projected to produce a discriminative combination of kernels. Eventually, the optimum kernel is given to the support vector machine classifier. Experiments have been conducted on two popular hyperspectral datasets (Indian Pines and Pavia University). For the datasets, the proposed algorithm gained 90.43% and 99.28% overall accuracy, respectively, using only 1% training samples, which is much better than the state-of-the-art MKL algorithm and deep learning-based approaches with lower computational time. [ABSTRACT FROM AUTHOR]

Approximate concept and graph theory are developed and applied to solve the integrated optimization problem of engineering structure containing both beam and plate discrete variables. Firstly, both structural responses and explicit requirements for process manufacturing are considered as constraints, which makes an optimization system based on the two-level multi-point approximation method more engineering oriented. Secondly, a practical evaluation method of topology rationality is proposed based on graph theory in order to avoid invalid structural analysis and improve optimization efficiency. The finite element model corresponding to the binary point-line relation in graph theory and judgements of force nodes, lump masses, structural integrity, etc. are unified. An engineering example shows that the two-level multi-point approximation method is still efficient in solving topology optimization problems with participating plates and beams, and the proposed topological rationality evaluation method can effectively eliminate about 15% of unreasonable configurations. [ABSTRACT FROM AUTHOR]

Graph theory effectively explains urban structures via street--street connectivity. However, systematic comparisons of street structures across cities remain challenging. This study employs graph convolutional networks (GCNs) to analyze street network structures. A two-branch GCN was used as the backbone to extract comparable features among street networks. The proposed approach was used to examine the structures of different urban road networks in a case study of polycentricity prediction across 298 Chinese cities. The model transformed approximately 4.5-million street segments into natural streets to create urban street graphs, which were subsequently analyzed to extract local and global embeddings. The extracted embeddings -- with a portion labeled with a known urban polycentricity score -- were used to predict the score for each city through a single-layer perceptron (SLP) model. Our results show consistency between the predicted polycentricity scores based on the derived street embeddings and those based on the population. Thus, the proposed GCN-based method can effectively predict the complexity and interconnection of street networks in different cities. This innovative integration of GCNs into urban studies demonstrates that deep learning techniques can analyze and comprehend the intricate patterns of street networks on a large scale. [ABSTRACT FROM AUTHOR]

The COVID-19 outbreak has revealed weaknesses in the supply chains (SCs) and how easily it can be influenced by these disruptions. Food supply chains (FSCs) is one of the most affected SCs, and it needs to be more resilient against SC disruptions because their vulnerable structure such as having perishable products. Therefore, this article aims to uncover the need for resilience in FSCs during the COVID-19 outbreak. For this purpose, the enablers of resilience on FSCs are determined after a detailed examination of the current literature. Then, the graph theory matrix approach has been used to reveal the relationships between these enablers and investigate importance of enablers of resilience in FSCs during COVID-19 outbreak. It is significant to determine preference of enablers and rank of importance to take actions effectively. Depending on the results, the rank orders of the enablers are classified as readiness, collaboration with stakeholders, IT alignment, risk aware, responsiveness, flexibility, appearance and sustainability, respectively. Suggested implications can be provided benefits for policymakers and managers in FSCs. [ABSTRACT FROM AUTHOR]

This article presents a new centrality measure. The presented measure was compared with state-of-the-art measures and proved to combines two features, low computational complexity and high precision of calculations. The measure has been mathematical analyzed, and then, experiments on real-life graphs were conducted. The mathematical analysis showed many essential properties of the proposed measure. Statistical analysis of the conducted experiment showed that measure has precision the same as state-of-the-art measures with much lower computational complexity. [ABSTRACT FROM AUTHOR]

A critical component of information security is data encryption, and numerous researchers have invented various approaches to encrypt data. This paper presents a novel image encryption approach using the shortest weight first algorithm from graph theory, categorized as a symmetric cipher where the user has much freedom in selecting the keys. Furthermore, this method requires no sophisticated computations and is simple to understand and implement while providing effective protection against cryptographic attacks, such as brute force. The detailed algorithm, analysis, and security implications are also presented. The results firmly set a good base for many real-world applications involving security. [ABSTRACT FROM AUTHOR]

Topological indices (TIs) have several biological applications in the treatment of blood cancer. TIs can be used to predict the efficacy of drugs in cancer treatment by providing information about the molecular structures of the drugs and their related properties. By analyzing the degree-based TIs of different drugs, researchers can identify the most effective drugs for treating specific types of blood cancer. Additionally, TIs can also be used to predict the toxicity of drugs, which is essential for developing safe and effective treatments. Furthermore, TIs can aid in the discovery and design of new drugs by providing insights into the relationship between molecular structure and biological activity. This article focuses on the applications of topological indices (TIs) in predicting the physical and biological properties of novel drugs used in the treatment of blood cancer. The drugs glasdegib, palbociclib, and daunorubicin are analyzed using degree-based topological indices computed through edge partitioning. A quantitative structure-property relationship (QSPR) model is then developed using linear regression to predict the properties such as boiling point (BP), flash point (FP), molar volume (MV), molecular weight, and complexity. The results demonstrate the potential of topological indices as a tool for drug discovery and design in the field of cancer treatment. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the problem of the exponential synchronisation for delayed neutral-type multi-weights complex networks (DNMCNs) with regime-switching jump diffusion under aperiodically intermittent control. Compared with the related works, hybrid time delays and regime-switching jump diffusion are introduced into neutral-type networks which can better simulate more complicated practical applications. The introduction of regime-switching jump diffusion increases the difficulties of synchronisation analysis in comparison with the Markovian jump diffusion. Meanwhile, it is noteworthy that we firstly extend the availability of aperiodically intermittent control scheme to handle the synchronisation issue with DNMCNs. On the basis of a technique that combines the Lyapunov method and graph theory, some sufficient criteria to synchronise DNMCNs via intermittent control are obtained. Finally, an oscillator system is considered as the application, and the corresponding numerical simulations are proposed to validate the applicability of the obtained theorems and show the effectiveness. [ABSTRACT FROM AUTHOR]

The Game of Cycles is a two-player impartial mathematical game, introduced by Francis Su in his book Mathematics for Human Flourishing (2020). The game is played on simple planar graphs in which players take turns marking edges using a sink-source rule. In Alvarado et al., the authors determine who is able to win on graphs with certain types of symmetry using a mirror-reverse strategy. In this paper, we analyze the game for specific types of cactus graphs using a modified version of the mirror-reverse strategy. [ABSTRACT FROM AUTHOR]

This study presents a unique method for network reconfiguration for Searching Maximum Loading Capacity Radial Network from an interconnected meshed network using continuation power flow. The network reconfiguration outcomes are also evaluated for various graph theory approaches presented in the literature. The combined graph theory and machine learning methods are used to determine the best sectional switch position. The system's radiality is verified using graph theory. The recommended technique is tested on a 30-node mesh network with 41 sectional switches. The results demonstrate that the distribution system can manage a higher connected load using the suggested Bayesian-Ridge approach while lowering total active and reactive power losses. [ABSTRACT FROM AUTHOR]

Chemical graph theory is an extension of mathematical chemistry that explores chemical phenomena and entities using the conceptual frameworks of graph theory. Chemical graph theory, in particular, uses chemical graphs to represent molecular structures. This chemical graph represents bonds and atoms, respectively, as edges and vertices. Cheminformatics predominantly uses chemical graphs as an essential data type for depicting chemical structures. The computable features of graphs lay the groundwork for (quantitative) structure-property and structure-activity predictions, which is an important component of cheminformatics. The physical and chemical characteristics of chemical compounds are thus reflected in these graphs, which can subsequently be reduced to graph-theoretical descriptors or indices. One of the most extensively researched distance-based graph descriptors is the resolving set W (metric dimension), which differentiates each pair of distinct vertices in every connected simple graph. The mixed metric dimension, which is the most significant variant of metric dimension, is determined for the complex molecular graph of a one-pentagonal carbon nanocone (PCN) in this manuscript. We show that only three distinct non-neighboring vertices (least possible requirement) from PCN can be adopted to uniquely identify all of the edges as well as vertices in PCN. [ABSTRACT FROM AUTHOR]

Sida rhombifolia also referred as "Bala" plant was found throughout the tropics and nurtures in warm climates and possesses various pharmacological properties like anti-diabetic, anti-inflammatory, antifungal, anti-arthritic, antibacterial and anti-diarrheal. We examine about eighteen bioactive phytochemicals from S.rhombifolia against Alzheimer's disease. The target proteins BACE1 and Aβ were selected based on graph theory network analysis. These eighteen bioactive compounds along with a known standard were docked against target proteins and their binding affinity falls between the range −3.7 Kcal/mol to −8.6 Kcal/mol. The top hit was observed for cryptolepine with a score of −8.3 Kcal/mol (BACE1) and −8.6 Kcal/mol (Aβ) followed by riboflavin with −8.1 Kcal/mol (BACE1) and 8.4 (Aβ). These two top-hit compounds were further investigated through frontier molecular orbitals to analyze the structural stability and reactivity using DFT/B3LYP–LanL2DZ basis set. The observed energy gap showed that cryptolepine (2.55786 eV) and riboflavin (3.3625 eV) exhibit better reactivity and its electrostatic potential map showed charge distribution over the atoms. The pharmacokinetic studies and toxicity analysis showed the drug-likeness and safety profile of cryptolepine and riboflavin. Further, the Ramachandran plot confirms the stability of the amino residues interacting with ligands. This study will support the use of Sida rhombifolia in conventional treatment and the beginning of the development of a novel drug against alzheimer's disease through in vitro model. [ABSTRACT FROM AUTHOR]

Chemical graph theory is an extension of mathematical chemistry that explores chemical phenomena and entities using the conceptual frameworks of graph theory. In particular, chemical graphs are used to represent molecular structures in chemical graph theory. Edges and vertices in this chemical graph substitute for bonds and atoms, respectively. The primary data types used throughout cheminformatics to depict chemical structures are chemical graphs. The basis for (quantitative) structure-property and structure-activity predictions, a central area of cheminformatics, is laid by the computable properties of graphs. The physical characteristics of molecules are thus reflected in these graphs, which can subsequently be reduced to graph-theoretical indices or descriptors. The resolving set Z , which distinguish every pair of distinct vertices in a connected simple graph, is one of the most well-studied distance-based graph descriptors. In this manuscript, we consider the most significant variation of a metric dimension known as partition dimension and determine it for the molecular complex graph of one-pentagonal carbon nanocone (PCN). We demonstrate that all of the vertices and edges in PCN can be uniquely identified only by considering three distinct non-neighboring partition sets (minimal requirement) from PCN. [ABSTRACT FROM AUTHOR]

The study of the characteristics and topologies of networks, including social, computer and biological networks, is known as graph theory. Numerous disciplines, such as epidemiology, which is the study of the transmission and management of infectious diseases like Covid-19, can benefit from the study of graph theory. Like, the first case of COVID-19 (Coronavirus) was reported in November of 2019; by the third week of April, 1,116,643 verified positive cases had been reported, with around 59,158 fatalities. All the meditational structures are symmetric, if we label to change the labels of graphs in either way the graph becomes symmetric and will be no change to it. So, there are many graph theoretical parameters to study the symmetric meditational structures, like metric and edge metric dimension. A notion known as edge metric dimension or edge metric basis states that with a chosen subset from the vertex set, known as the edge resolving set, the whole edge set of a structure uniquely recognised. This idea of vertices resolvability allows for the distinct identification of COVID antiviral medication structures and aids in the research of the structure's structural characteristics. The chosen resolving set and the computed edge metric dimension will be invariant due to the symmetry of the graphs. Arbidol, malaria, carboxylic, thalidomide and theaflavin are the names of these compounds which are discussed in this work. [ABSTRACT FROM AUTHOR]

Complex networks are difficult to understand and deal with, yet building a graph of any complex and huge structure, whether chemical or computer-related, is quite straightforward. In the form of a graph theory view, it becomes simple to design networks. Each component's recognition is aided by the ease of its production in the form of graph theory. Finding a vertex (node or atom) in a structure is similarly difficult; in this instance, resolvability parameters come into play. This technique plays a significant role in managing or allowing access to each vertex in relation to some chosen vertices called a resolving set that shapes an entire cluster of vertices into a unique form and every single vertex is easy to recognise or locate, whether the small or large the structure. This article contributes the bounds on the parameter of partition dimension of chemical complexes in dialkyltin of supramolecular chain from N-Salicylidene-L-Valine. We supposed the complexes of chains from 2,3,4 and another chemical network, and we demonstrated that the number of vertices has a significant impact on the composition of resolving partition sets. [ABSTRACT FROM AUTHOR]

Stormwater management systems rely on an acyclic network structure, making the network more vulnerable to failure. Existing stormwater resilience studies have predominantly focused on hydraulic and hydrological characteristics of the system with no robust frameworks to evaluate the resilience of the stormwater piped network in terms of network connectivity. This paper introduces a new index-based quantitative framework to characterise the resilience of acyclic stormwater network structure using graph theory and resilience theories. This includes an index developed to evaluate the overall independency of a pipe within an acyclic piped network. The framework was applied to various simple network structures, and an existing stormwater network demonstrating the influence of network structure, pipeline connectivity and number of outlets on the network resilience. This framework can be used to test different network layouts and structures in urban design and pipeline renewal projects to maximise the resilience of the structure of stormwater networks. [ABSTRACT FROM AUTHOR]

In this article, a novel dynamic periodic event-triggered control (DPE-TC) is proposed to investigate input-to-state stability (ISS) in multilayer coupled systems (MCSs). Different from the existing literature, a dynamic term is introduced to event-triggered control (E-TC), which can reduce the number of event triggers as the interexecution times are prolonged on the whole. Moreover, a periodic sampling is adopted, from where the Zeno phenomenon is naturally avoided. Based on the Lyapunov method and graph theory, ISS for coupled systems under the DPE-TC is established. Meanwhile, a dynamic event-triggered control with dwell-time is proposed, and a corollary to ensure the ISS of MCSs is also provided. Eventually, results are applied to second-order oscillators and a numerical example is given to prove the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

The localisation of a network is the process of gaining access to a node's precise location or position. Using this technology, it is possible to determine the exact position of each network node in terms of a select few nodes within a subset. The locating set of a network is this subset, and the locating number of a network is its lowest cardinality. While the edge locating number is the same concept but on the bonds instead of nodes. In this work, we discussed some resolvability parameters such as locating number, edge locating number, fault-tolerant locating number and partition locating number of honeycomb rectangular torus. The honeycomb rectangular torus is very effective and innovative structure in chemical graph theory. This type of structure is being used in image processing, cellular phone base stations, computer graphics and more in mathematical chemistry. [ABSTRACT FROM AUTHOR]

Functional connectivity (FC) measures statistical dependence between cortical brain regions. Studies of FC facilitate understanding of the brain's function and architecture that underpin normal cognition, behavior, and changes associated with various factors (e.g. nutritional supplements) at a large scale. We aimed to identify modifications in FC patterns and targeted brain anatomies in piglets following perinatal intake of different nutritional diets using a graph theory based approach. Forty-four piglets from four groups of pregnant sows, who were treated with nutritional supplements, including control diet, docosahexaenoic acid (DHA), egg yolk (EGG), and DHA + EGG, went through resting-state functional magnetic resonance imaging (rs-fMRI). We introduced the use of differential degree test (DDT) to identify differentially connected edges (DCEs). Simulation studies were first conducted to compare the DDT with permutation test, using three network structures at different noise levels. DDT was then applied to rs-fMRI data acquired from piglets. In simulations, the DDT showed a greater accuracy in detecting DCEs when compared with the permutation test. For empirical data, we found that the strength of internodal connectivity is significantly increased for more than 6% of edges in the EGG group and more than 8% of edges in the DHA and DHA + EGG groups, all compared to the control group. Moreover, differential wiring diagrams between group comparisons provided means to pinpoint brain hubs affected by nutritional supplements. DDT showed a greater accuracy of detection of DCEs and demonstrated EGG, DHA, and DHA + EGG supplemented diets lead to an improved internodal connectivity in the developing piglet brain. [ABSTRACT FROM AUTHOR]

The present article is devoted to discuss the pth moment exponential ultimate boundedness for a class of stochastic distributed delay-coupled systems on networks driven by G-Brownian motion. By combining the method of proof by contradiction with Lyapunov method and graph theory, some sufficient condition for both the Lyapunov-type theorem and the coefficients-type theorem are proposed to ensure the pth moment exponential ultimate boundedness of the considered systems. As applications, the boundedness criteria are applied to stochastic distributed delay-coupled neural networks and stochastic distributed delay-coupled control systems in the framework of G-Brownian motion. [ABSTRACT FROM AUTHOR]

A famous theorem in graph theory—originating with Euler—characterizes connected even-degree graphs as (1) those graphs that admit an Euler tour, and (2) those connected graphs that decompose as a face-disjoint union of cycles. We explore a 2-dimensional generalization of this theorem, with graphs (i.e., 1-complexes) replaced by 2-complexes. This entails an interesting generalization of cycles, and the introduction of the notion of a "2-dimensional Euler tour." [ABSTRACT FROM AUTHOR]

In this paper, a new structural design method based on MATLAB is developed for the configuration design and optimization of real-life planar manipulators in the high-speed press line. To explore planar manipulators with better performance, the developed method provides a suite of analysis procedures including demonstrating structural synthesis in graph theory, building conversion relations between different models, and generating new configurations of the planar manipulator. In the structural synthesis, the whole family of non-isomorphism planar 8-link kinematic chains with up to 3 prismatic pairs is generated, which lays a solid foundation for the generation of new configurations of planar manipulators. Under the expected requirements and constraints, the original planar manipulator is compared with new planar manipulators in which the developed method. The result shows that the developed method of task-driven structural synthesis is effective in generating configurations of planar manipulators and enriches related research of structural design and optimization in the field. [ABSTRACT FROM AUTHOR]

Hydrogen-bonded networks in 1-propanol-methanol binary mixture are studied using molecular dynamics simulation along with experimental techniques (FTIR, dielectric spectroscopy and refractive index measurements) for the entire concentration range. The structure of hydrogen-bonded networks is studied through radial distribution function, hydrogen bond statistics and graph theoretical analysis from molecular dynamics. It is observed that the probability of hydrogen bonding is maximum in methanol molecules followed by hydrogen bonding between methanol and 1-propanol molecules and minimum among 1-propanol molecules, as the concentration changes. The graph theory results show the formation of linear chain hydrogen bond networks, with no caged structures, which is validated from the experimental results. Further, the deconvolution of the FTIR OH peak suggests the presence of linear multimers in all concentrations of the binary system. Average degree of the hydrogen-bonded networks from graph theory indicates a complex networks among pure alcohols and dimers between methanol and 1-propanol in their binary mixtures at all concentrations. The negative values of excess permittivity indicate that the components of the mixture interact in a manner such that the net dipole polarisation decreases. [ABSTRACT FROM AUTHOR]

In this study, we investigate students’ mathematical thinking of the tree concept, a fundamental concept in graph theory, using a combination of the APOS theory and Tall’s three worlds of mathematics. The qualitative research describes here is a phenomenological study drawing on task-based interviews with 18 undergraduate mathematics students. The findings indicate that students preferred to think in the embodied world when solving tasks related to the tree concept. This type of thinking, despite its great value, should not prevent students from thinking in the symbolic and formal worlds. Furthermore, the findings indicate that almost half of the participants had difficulties with the acyclicity and connectivity concepts, which are necessary prior knowledge to help students develop Process and Object for the tree concept. The results also suggest that more opportunities could be provided for students to engage with tasks that related to Process and Object in the three mathematics worlds. [ABSTRACT FROM AUTHOR]

This paper considers the stabilisation of high-order nonlinear stochastic delayed coupled systems with Markovian switching (HNSMS) by periodically intermittent control (PIC). Notably, the coefficients in HNSMS no longer satisfy the linear growth condition. In the mean time, PIC is first introduced to ensure the stabilisation of HNSMS. Since current Halanay-type differential inequalities (H-type inequalities) are not applicable to high-order nonlinear systems with PIC, a generalised H-type inequality with high-order terms for such systems is established, in which the order of high-order terms can be different. Together with graph theory and Lyapunov method, some sufficient conditions reaching the stability are presented. Then, our results are used to study the stability of modified Van der Pol–Duffing oscillators with Markovian switching. Ultimately, the effectiveness of theoretical results is checked by a numerical test. [ABSTRACT FROM AUTHOR]

In this paper we investigate bottlenecks in adaptive dynamic surface control (DSC) and unveil an innovative consensus tracking controller to track the desired trajectory for a class of fractional-order multi-agent systems with non-linear dynamics. The study derives an algorithm by implementing graph theory and the DSC method. The main approaches in the control of fractional-order systems are the DSC and the adaptive DSC techniques to avoid the computational complexity of fractionalorder virtual control law. According to these techniques, a virtual control law is formulated and the proposed controller is passed through a fractional-order dynamic surface. By employing the DSC and adaptive DSC laws, we demonstrate that the desired consensus tracking between agents can be ensured. To verify the performance of the new approach, we simulate the desirable scenarios and evaluate the results against a popular adaptive sliding mode technique. [ABSTRACT FROM AUTHOR]

Risk assessment is a vital part in project management. It is possible that experts may provide comprehensive linguistic preference information in distinct forms with respect to different aspects of the risk assessment problem in investment management. It is a challenge to model and deal with comprehensive linguistic preference assessments in multiple forms given by experts. In this regard, this paper defines the generalised probabilistic linguistic preference relation (GPLPR) to represent different forms of linguistic preference information in a unified structure. Then, a probability cutting method is proposed to simplify the representation of a GPLPR. Afterwards, a graph-theory-based method is developed to improve the consistency degree of a GPLPR. A group decision making method with GPLPRs is then proposed to carry on the risk assessment in project management. Discussions regarding the comparative analysis and managerial insights are given. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) optical systems have been recently deployed for the assessment of 3D topography of finished products during manufacturing processes. Although the 3D topographic data contain rich information about the product and manufacturing processes, existing monitoring approaches are incapable of capturing the complex characteristics between the topographic values, which makes them ineffective in detecting local and spatial surface faults. We develop a spatially weighted graph theory-based approach for accurate monitoring of 3D topographic surfaces. We imporove the representation of surface characteristicsby proposing the in-control multi-region surface segmentation algorithm, which segments the observed topographic pixels into clusters according to the information learned from in-control surfaces. We propose the maximum local spatial randomness feature for the effective description of local and spatial topographic characteristics. After representing the surface characteristics as a spatially weighted graph network, we monitor its connectivity through the developed spatial graph connectivity statistic. The proposed approach is robust in detecting and locating different forms of local and spatial faults that appear on simulated and real-life topographic surfaces and outperforms the existing monitoring approaches. [ABSTRACT FROM AUTHOR]

Abstract–We prove a few results about non-nilpotent graphs of symmetric groups Sn – namely that they satisfy a conjecture of Nongsiang and Saikia (which is likewise proved for alternating groups An), and that for n ⩾ 19 each vertex has degree at least n ! 2 . We also show that the class of non-nilpotent graphs does not have any "local" properties, i.e. for every simple graph X there is a group G, such that its non-nilpotent graph contains X as an induced subgraph. [ABSTRACT FROM AUTHOR]

Vertical handovers (VH) is said to be a significant effect of user mobility in a diverse wireless network as it causes a major effect on network performances, like call blocking probability, packet delay, or throughput. On the other hand, the analysis of VH meets a lot of complexities when it comes to investigation, including network modeling that was very complex owing to the diversity in topology. This article aims to present a VH method by means of graph theory. At first, the improved k-partite graph is exploited to model the VH issues in HetNets. Second, improved Dijkstra's algorithm (DA) is deployed for choosing the best path. Further, the analytic hierarchy process is used for estimating the adaptive weights among nodes. Accordingly, optimal selection of weights in DA is performed depending on a hybridized model named as grey wolf upgraded CSO. Ultimately, several metrics such as throughput, packet jitter, and delay and packet losses indicate that the created strategy is efficient. [ABSTRACT FROM AUTHOR]

Mild cognitive Impairment (MCI) is notoriously heterogenous in terms of clinical presentation, neuroimaging correlates, and subsequent progression. Predicting who will progress to dementia, which type of dementia, and over what timeframe is challenging. Previous work has attempted to identify MCI subtypes using neuropsychological measures in an effort to address this challenge; however, there is no consensus on approach, which may account for some of the variability. Using a hierarchical community detection approach, we examined cognitive subtypes within an MCI sample (from the Alzheimer's Disease Neuroimaging Initiative [ADNI] study). We then examined whether these subtypes were related to biomarkers (e.g., cortical volumes, fluorodeoxyglucose (FDG)-positron emission tomography (PET) hypometabolism) or clinical progression. We identified five communities (i.e., cognitive subtypes) within the MCI sample: 1) predominantly memory impairment, 2) predominantly language impairment, 3) cognitively normal, 4) multidomain, with notable executive dysfunction, 5) multidomain, with notable processing speed impairment. Community membership was significantly associated with 1) cortical volume in the hippocampus, entorhinal cortex, and fusiform cortex; 2) FDG PET hypometabolism in the posterior cingulate, angular gyrus, and inferior/middle temporal gyrus; and 3) conversion to dementia at follow up. Overall, community detection as an approach appears a viable method for identifying unique cognitive subtypes in a neurodegenerative sample that were linked to several meaningful biomarkers and modestly with progression at one year follow up. [ABSTRACT FROM AUTHOR]

The local independence assumption states that variables are unrelated after conditioning on a latent variable. Common problems that arise from violations of this assumption include model misspecification, biased model parameters, and inaccurate estimates of internal structure. These problems are not limited to latent variable models but also apply to network psychometrics. This paper proposes a novel network psychometric approach to detect locally dependent pairs of variables using network modeling and a graph theory measure called weighted topological overlap (wTO). Using simulation, this approach is compared to contemporary local dependence detection methods such as exploratory structural equation modeling with standardized expected parameter change and a recently developed approach using partial correlations and a resampling procedure. Different approaches to determine local dependence using statistical significance and cutoff values are also compared. Continuous, polytomous (5-point Likert scale), and dichotomous (binary) data were generated with skew across a variety of conditions. Our results indicate that cutoff values work better than significance approaches. Overall, the network psychometrics approaches using wTO with graphical least absolute shrinkage and selector operator with extended Bayesian information criterion and wTO with Bayesian Gaussian graphical model were the best performing local dependence detection methods overall. [ABSTRACT FROM AUTHOR]

Boron clusters are small, three-dimensional structures made of boron atoms. These come in a wide range of shapes and sizes, from basic planar constructions to complex polyhedral patterns. Boron clusters are fascinating from both a fundamental and practical perspective because of their unique electrical, optical, and chemical properties. More focus has lately been placed on boron cluster sheets, which are two-dimensional structures made of boron clusters. Quantitative structure-activity relationship (QSAR) studies implement M-polynomials, a type of molecular descriptor, to describe the topology of molecules. These are based on the notion of graph theory, which provides a theoretical framework for quantitatively studying molecular graphs. In this article, we discussed some novel topological descriptors-based M-polynomials and found algebraic formulations for the boron cluster or borophene sheets. We discussed first Zagreb, second Zagreb and Randić M-polynomials, based on the different differential and integral operators. [ABSTRACT FROM AUTHOR]

To mitigate urban drainage network pressures and seek sustainable solutions, novel tools like graph theory are presently being studied. This paper presents a systematic literature review of graph-based approaches through an intensive content analysis based on 144 published papers. Comparisons are drawn between water distribution networks and urban drainage networks in terms of convergence and divergence, revealing more divergence in network topological characteristics but more convergence in functional features. The findings provide convincing evidence for applications in UDNs, despite limited numbers and depth. Subsequently, a comparison between graph-based and hydraulic-based approaches is shown, demonstrating distinct advantages of graph-based methods in cases with limited data and time constraints. Based on these findings, the paper suggests several potential directions, including the improvement of parameter calculation formulas, the definition of parameter mathematical ranges and the popularization of recommended values. Finally, the paper examines its own shortcomings. [ABSTRACT FROM AUTHOR]