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The topological indices provide quantitative structural characteristics of drug molecules that can be utilized to predict or establish correlations with the biological activity, physicochemical properties, and toxicity of the molecules. Such studies play a crucial role in the initial stages of drug development by aiding in the identification and optimization of potential drug candidates and providing cost-effective techniques for experimental studies. Cancer, a multifaceted disease, can originate in any part of the body due to various factors, including genetic mutations, environmental toxins, and lifestyle choices. Blood cancer, encompassing malignancies affecting the blood, bone marrow, and lymphatic systems, is the focus of this research paper. The current study investigates a comprehensive set of drugs employed in blood cancer treatment, including clofarabine, mercaptopurine, olutasidenib, glasdegib, gliteritinib, zanubrutinib, chlorambucil, ibrutinib, bosutinib, hydroxyurea, cyclophosphamide, doxorubicin, daunorubicin, ivosidenib, prednisone, busulfan, omacetaxine mepesuccinate, and asciminib. By conducting a thorough analysis of these drugs, we acquire valuable insights into their molecular properties, which are crucial for predicting their behavior and efficacy in blood cancer treatment. We have devised QSPR models by leveraging the reverse degree and entropy topological indices. Our proposed QSPR models are compared with existing degree-based models, emphasizing the superior effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Topological descriptors are widely utilized as graph theoretical measures for evaluating the physicochemical properties of organic frameworks by examining their molecular structures. Our current research validates the usage of topological descriptors in studying frameworks such as metal-butylated hydroxytoluene, NH-substituted coronene transition metal, transition metal-phthalocyanine, and conductive metal-octa amino phthalocyanine. These metal organic frameworks are crucial in nanoscale research for their porosity, adaptability, and conductivity, making them essential for advanced materials and modern technology. In this study, we provide the topological and entropy characterizations of these frameworks by employing robust reverse degree based descriptors, which offer insightful information on structural complexities. This structural information is applied to predict the graph energy of the considered metal organic frameworks using statistical regression models. [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. [ABSTRACT FROM AUTHOR]

This study investigates the quantitative structure-property relationship (QSPR) modeling of guar gum biomolecules, focusing on their structural parameters. Guar gum, a polysaccharide with diverse industrial applications, exhibits various properties such as viscosity, solubility, and emulsifying ability, which are influenced by its molecular structure. In this research, M-polynomial and associated topological indices are employed as structural descriptors to represent the molecular structure of guar gum. The M-polynomial and associated topological indices capture important structural features, including size, shape, branching, and connectivity. By correlating these descriptors with experimental data on guar gum properties, predictive models are developed using regression analysis techniques. The analysis revealed a strong correlation between the boiling point and molecular weight and all the considered topological descriptors. The resulting models offer insights into the relationship between guar gum structure and its properties, facilitating the optimization of guar gum production and application in various industries. This study demonstrates the utility of M-polynomial and QSPR modeling in elucidating structure-property relationships of complex biomolecules like guar gum, contributing to the advancement of biomaterial science and industrial applications. [ABSTRACT FROM AUTHOR]

In this article, a quantitative structure-property relationship is performed for the prediction of six physico-chemical properties of 16 alkaloid structures using three different types of degree-based topological indices. Chemical structures are considered as graphs, where elements are taken as vertices and bounds between them are taken as edges. We defined two new degree-based topological indices, namely, the "modified harmonic index" and the "advanced harmonic index," to analyze and examine the properties of alkaloids. The topological indices and experimental values act as the inputs of linear and quadratic regression models. The correlation values and p-values for all the indices are significant which describe the validity and usefulness of the results. The outcomes determined in this article assist pharmacists and chemists in studying the structures of alkaloids for use in daily life, agriculture, pharmacy, and industries. The study of chemical structures with the help of molecular descriptors and regression models is a theoretical method that saves time and money. [ABSTRACT FROM AUTHOR]

The edge k -labeling ψ of G is defined by a mapping from E G to a set of integers 1 , 2 , ... , k , where the integer weight assigned to the vertex x ∈ V G is given as w ψ x = ∑ ψ x y , such that the sum is taken over every vertex of y ∈ V G that is adjacent to x and the integer weights of adjacent vertices must be distinct for all vertices with x ≠ y. An irregular assignment of G using atmost k labels which is considered to be a minimum k is defined as irregularity strength of a graph G and can be denoted as s G . There are also further works on familiar irregular assignments, such as edge irregular labelings, vertex irregular total labelings, edge irregular total labelings, and face irregular entire k -labelings of plane graphs. A plane graph can be defined as a graph that is embedded in the plane in which no two lines will be intersected. In a plane graph the number of regions present are called faces and we denote it as F. The concept of total face irregularity strength is defined by the motivation of irregular networks and entire irregular face k -labeling. In our paper, we have obtained a minimum bound for the total face irregularity strength of two-connected plane graphs like cycle-of-ladder, C -necklace graph, P -necklace graph, sibling tree, and triangular graph. [ABSTRACT FROM AUTHOR]

Carbon nanorings are macrocyclic aromatic hydrocarbons that represent the segments of carbon nanotubes and have received considerable attention due to their novel nanoelectronic and photophysical capabilities. The cycloparaphenylene (CPP), a carbon nanoring with a ring-like structure comprising of only benzene units, has been the subject matter of several studies. The carbon nanoring structures bearing polycyclic aromatic hydrocarbons such as hexabenzocoronene and pyrene molecules are also found to exhibit exciting characteristics and applications. This in turn evolves a wide range of novel chemical structures whose behavior and attributes are to be studied and explored. Molecular descriptors help us to study such novel nanostructures by providing a greater understanding of their unique properties, whereas such characterization remains challenging due to their ring-shaped arrangement. In this study, we investigate cycloparaphenylene series and show that such structures are not bounded by the partial cube family. We also derive the exact analytic expressions of degree, distance and closeness-related descriptors. We have also computed the thermodynamic and kinetic stabilities of the three structures using the graph spectra, resonance energies, HOMO-LUMO gaps and Kekulé counts obtained from the graph spectra and combinatorial methods. Whereas the CPPhbc[5] structure is thermodynamically more stable, the CPPyr[9] is kinetically more stable. Furthermore, we have employed combinatorial generating function methods to compute the NMR and ESR spectra of the title compounds. [ABSTRACT FROM AUTHOR]

Porous two‐dimensional (2D) nanographene structures are materials with vast potentials in several areas of research with varied applications. The porous structures of these 2D‐materials offer multiple applications in the field of nanochemistry including sequestration of toxic metal ions as they possess large surface areas, enhanced electrical and electronic properties, and high mechanical flexibility. Their porous structures facilitate the creation of highly efficient electrodes, which could significantly improve the performance of batteries and other energy storage technologies. Topological descriptors are powerful tools for characterizing their structures and predicting the properties of molecules and thus have a number of applications. We compute the analytical expressions for degree‐based and Szeged‐type topological descriptors and their information‐theoretic entropies. In addition, we perform a comparative analysis of the scaled bond‐wise entropies between nanoporous graphenes and rectangular kekulene structures with comparable sizes. Furthermore, we predict the 13C and proton NMR spectral patterns of these materials using graph‐theoretical techniques. [ABSTRACT FROM AUTHOR]