Neighborhood degree sum-based molecular descriptors of fractal and Cayley tree dendrimers

3D molecular structural modeling and characterization of indium phosphide via irregularity topological indices

Indium phosphide (InP) is a binary semiconductor composed of indium and phosphorus. It has a zinc blende crystal structure, which is a type of cubic lattice structure. This lattice is composed of indium and phosphorus atoms arranged in a lattice of cube-shaped cells, with each cell containing four indium atoms and four phosphorus atoms. This lattice structure is the same for all materials with a zinc blende crystal structure and is the most common type of lattice structure in semiconductors. Indium phosphide (InP) has several chemical applications. It is commonly used as a dopant in the production of semiconductors, where it helps control the electrical properties of the material. InP is also utilized in the synthesis various indium-containing compounds, which can have applications in catalysts and chemical reactions. Additionally, InP nanoparticles have been investigated for their potential use in biomedical imaging and drug delivery systems. The topological characterization of 3D molecular structures can be performed via graph theory. In graph theory, the connections between atoms are represented as edges and the atoms themselves are represented as nodes. Furthermore, graph theory can be used to calculate the topological descriptors of the molecule such as the degree-based and reverse degree-based irregularity toplogical indices. These descriptors can be used to compare the topology of different molecules. This paper deals with the modeling and topological characterization of indium phosphide ( InP ) via degree-based and reverse irregularity indices. The 3D crystal structure of the InP is topologically modeled via partition of the edges, and derived closed form expressions for its irregularity indices. Our obtained results will be surely be helpful in investigating the QSPR/QSAR analysis as well as understanding the deep irregular behavior of the indium phosphide ( InP ) .

Potential application of novel AL-indices as molecular descriptors

A topological index or a descriptor is a graph invariant that describes the structure of a graph as a numerical value. This paper proposes eight novel indices called AL-indices, based on distance and degree, and analyzes their behavior to show that they can serve as potentially useful molecular descriptors. We find that among the proposed indices many have very good discriminative power when compared to the existing vertex-degree based indices and justifies the requirement of these new indices. Further, we propose a method to compute these indices and vertex-degree-based indices from a recently proposed graph matrix, referred to as neighborhood matrix. Computationally, we correlate the proposed indices' efficiency against the octane isomers' and polychlorobiphenyls' physicochemical properties. We perform a comparative study of these indices with a few well-known vertex degree-based indices. Further, the proposed indices' discriminative capacity is analyzed and shown to have higher discriminative power on the considered datasets. Among all the indices under study, four indices, namely AL₄, AL₅, AL₇, and AL₈ have shown the highest discriminative power on the set of octane isomers. While the indices AL₄ and AL₇ have the highest discriminative power on the set of PCB molecules compared to the other VDB indices. Among the proposed and considered indices, we show that the first index AL₁ has a good correlation with the Acentric factor and entropy of octane isomer and with the total surface area, log-water-solubility, relative retention time, octanol-water-partition, and log-water-activity coefficient of PCBs.

On ve-Degree Irregularity Index of Graphs and Its Applications as Molecular Descriptor

Most of the molecular graphs in the area of mathematical chemistry are irregular. Therefore, irregularity measure is a crucial parameter in chemical graph theory. One such measure that has recently been proposed is the ve-degree irregularity index (irrve). Quantitative structure property relationship (QSPR) analysis explores the capability of an index to model numerous properties of molecules. We investigate the usefulness of the irrve index in predicting different physico-chemical properties by carrying out QSPR analysis. It is established that the irrve index is efficient to explain the acentric factor and boiling point of molecules with powerful accuracy. An upper bound of irrve for the class of all trees is computed with identifying extremal graphs. We noticed that the result is not correct. In this report, we provide a counter example to justify our argument and determine the correct outcome.

On Neighborhood Inverse Sum Indeg Energy of Molecular Graphs

The spectral graph theory explores connections between combinatorial features of graphs and algebraic properties of associated matrices. The neighborhood inverse sum indeg (NI) index was recently proposed and explored to be a significant molecular descriptor. Our aim is to investigate the NI index from a spectral standpoint, for which a suitable matrix is proposed. The matrix is symmetric since it is generated from the edge connection information of undirected graphs. A novel graph energy is introduced based on the eigenvalues of that matrix. The usefulness of the energy as a molecular structural descriptor is analyzed by investigating predictive potential and isomer discrimination ability. Fundamental mathematical properties of the present spectrum and energy are investigated. The spectrum of the bipartite class of graphs is identified to be symmetric about the origin of the real line. Bounds of the spectral radius and the energy are explained by identifying the respective extremal graphs.

NM-polynomials and Topological Indices of Some Cycle-Related Graphs

Topological indices (molecular descriptors) are numerical values of a chemical structure and represented by a graph. Molecular descriptors are used in QSPR/QSAR modeling to determine a chemical structure’s physical, biological, and chemical properties. The cycle graphs are symmetric graphs for any number vertices. In this paper, recently defined neighborhood degree sum-based molecular descriptors and polynomials are studied. NM-polynomials and molecular descriptors of some cycle-related graphs, which consist of the wheel graph, gear graph, helm graph, flower graph, and friendship graph, are computed and compared.