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In this study, the authors discuss the vertex congestion of any embedding from the guest graph into the host graph and outline a rigorous mathematical method to compute the wirelength of that embedding. Further, they show that the computation of the optimal wirelength depends on finding optimal solutions for another graph partition problem such as edge isoperimetric problem in that guest graph. On the other side, they consider an important variant of the popular hypercube network, the enhanced hypercube, and obtain the nested optimal solutions for the edge isoperimetric problem. As a combined output, they illustrate the authors' technique by embedding enhanced hypercube into a caterpillar and from that reducing the linear layout of the enhanced hypercube. As another application of their technique, they embed the hypercube as well as the enhanced hypercube on the two rows extended grid structure with optimal wirelength for the first time and showing that the existing edge congestion technique cannot be used to solve this problem. [ABSTRACT FROM AUTHOR]

The hypercube network is one of the most popular parallel computing networks since it has a simple structure and is easy to implement. The locally twisted cube is a newly introduced variant of the hypercube which has the same number of nodes and same number of connections per node as the hypercube, but has only half the diameter and better graph embedding capability as compared to hypercube. In this paper, we show that ann-dimensional locally twisted cube is constructed by forming a matching between the nodes of two disjoint copies of an-dimensional hypercube. In addition, we embed the locally twisted cube into path with minimum layout. [ABSTRACT FROM PUBLISHER]

The edge‐Wiener index is conceived in analogous to the traditional Wiener index and it is defined as the sum of distances between all pairs of edges of a graph G. In the recent years, it has received considerable attention for determining the variations of its computation. Motivated by the method of computation of the traditional Wiener index based on canonical metric representation, we present the techniques to compute the edge‐Wiener and vertex‐edge‐Wiener indices of G by dissecting the original graph G into smaller strength‐weighted quotient graphs with respect to Djoković‐Winkler relation. These techniques have been applied to compute the exact analytic expressions for the edge‐Wiener and vertex‐edge‐Wiener indices of coronoid systems, carbon nanocones and SiO2 nanostructures. In addition, we have reduced these techniques to the subdivision of partial cubes and applied to the circumcoronene series of benzenoid systems. [ABSTRACT FROM AUTHOR]

Phthalocyanine derivative nanostructures are highly organized organometallic structures that exhibit two-dimensional polymeric phthalocyanine frameworks. These conjugated macrocycles, characterized by their versatility, have gained significant attention in the development of technologies due to their structural resemblance to naturally occurring porphyrin complexes. The growth of these structures is analyzed to explore their topological characteristics by employing connectivity-based bond additive descriptors. The generated results are utilized in conjunction with the selected samples from Chem3D software to establish predictive models for calculating log P , log S , polar surface area, and total energy. Moreover, the structural complexity of these frameworks is compared through classical, spectral, and topological index based entropies, with the identification of the advantages and disadvantages associated with each of the three approaches. [Display omitted] [ABSTRACT FROM AUTHOR]

Nanostructures are tiny objects at the molecular and microscopic scale, with carbon nanotubes being the most notable among them. The elements possess exceptional microelectronic properties and other unique characteristics. Researchers have recently focused on the mathematical features of these materials. Molecular descriptors are crucial in mathematical chemistry, particularly in QSAR and QSPR modeling. Topological indices hold a significant position among them. This study presents the precise formulation of the ten most crucial topological indices for a benzene ring positioned on a P-type surface within the highly symmetric 2D lattice BCZ 48 . We have incorporated the computed indices to develop a predictive model for the graph energy of the 2D lattice and, in addition, provided the NMR patterns and the HOMO-LUMO gap., (© 2024. The Author(s).)

Global health concerns persist due to the multifaceted nature of heart diseases, which include lifestyle choices, genetic predispositions, and emerging post-COVID complications like myocarditis and pericarditis. This broadens the spectrum of cardiovascular ailments to encompass conditions such as coronary artery disease, heart failure, arrhythmias, and valvular disorders. Timely interventions, including lifestyle modifications and regular medications such as antiplatelets, beta-blockers, angiotensin-converting enzyme inhibitors, antiarrhythmics, and vasodilators, are pivotal in managing these conditions. In drug development, topological indices play a critical role, offering cost-effective computational and predictive tools. This study explores modified reverse degree topological indices, highlighting their adjustable parameters that actively shape the degree sequences of molecular drugs. This feature makes the approach suitable for datasets with unique physicochemical properties, distinguishing it from traditional methods that rely on fixed degree approaches. In our investigation, we examine a dataset of 30 drug compounds, including sotagliflozin, dapagliflozin, dobutamine, etc., which are used in the treatment of cardiovascular diseases. Through the structural analysis, we utilize modified reverse degree indices to develop quantitative structure-property relationship (QSPR) models, aiming to unveil essential understandings of their characteristics for drug development. Furthermore, we compare our QSPR models against the degree-based models, clearly demonstrating the superior effectiveness inherent in our proposed method., (© 2024. The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.)

A carbon-based material with a broad scope of favourable developments is called graphene. Recently, a graphene nanoribbon with cove-edged was integrated by utilizing a bottom-up liquid-phase procedure, and it can be geometrically viewed as a hybrid of the armchair and the zigzag edges. It is indeed a type of nanoribbon containing asymmetric edges made up of sequential hexagons with impressive mechanical and electrical characteristics. Topological indices are numerical values associated with the structure of a chemical graph and are used to predict various physical, chemical, and biological properties of molecules. They are derived from the graph representation of molecules, where atoms are represented as vertices and bonds as edges. In this article, we derived the exact topological expressions of cove-edged graphene nanoribbons based on the graph-theoretical structural measures that help reduce the number of repetitive laboratory tasks necessary for studying the physicochemical characteristics of graphene nanoribbons with curved edges., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors.)

Background: Cheminformatics is a fascinating emerging subfield of chemical graph theory that studies quantitative structure-activity and property relationships of molecules and, in turn, uses these to predict the physical and chemical properties, which are extremely useful in drug discovery and optimization. Knowledge discovery can be put to use in pharmaceutical data matching to help in finding promising lead compounds., Method: Topological descriptors are numerical quantities corresponding to the chemical structures that are used in the study of these phenomena., Result: This paper is concerned with developing the generalized analytical expression of topological descriptors for zeolite ACO structures with underlying degree and degree-sum parameters., Conclusion: To demonstrate improved discrimination power between the topological descriptors, we have further modified Shannon's entropy approach and used it to calculate the entropy measures of zeolite ACO structures., (Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.net.)

Entropy of a connected network is a quantitative measure from information theory that has triggered a plethora of research domains in molecular chemistry, biological sciences and computer programming due to its inherent capacity to explore the structural characteristics of complex molecular frameworks that have low structural symmetry as well as high diversity. The analysis of the structural order is greatly simplified through the topological indices based graph entropy metrics, which are then utilized to predict the structural features of molecular frameworks. This predictability has not only revolutionized the study of zeolitic frameworks but has also given rise to new generations of frameworks. We make a comparative study of two versatile framework topologies namely zeolites BCT and DFT, which have been widely utilized to create a new generation of frameworks known as metal organic frameworks. We discuss bond-additive topological indices and compute entropy measure descriptors for zeolites BCT and DFT using degree and degree-sum parameters. In addition, we perform bond-wise scaled comparative analysis between BCT and DFT which shows that zeolite BCT has greater entropy values compared to zeolite DFT., (© 2023. The Author(s).)