The degree of a vertex of a molecular graph is the number of first neighbors of this vertex. A large number of molecular-graph-based structure descriptors (topological indices) have been conceived, ...depending on vertex degrees. We summarize their main properties, and provide a critical comparative study thereof. (doi: 10.5562/cca2294) Keywords: topological index, molecular structure descriptor, vertex-degree-based topological index, molecular graph, chemical graph theory
Following the symmetric division deg index, this article introduces a new graph index called the SDE index which is based on the eccentrity of vertices. Also, the eccentric version of the extended ...adjacency matrix is defined. We establish several results regarding the properties of the extended eccentric matrix and spectra of different classes of graphs including trees and unicyclic graphs. Some new bounds also for the minimum spectral radius of the extended eccentric matrices were determined. Besides, we present bounds for the extended eccentric spectral radius of path graph and prove that the maximum value of the extended eccentric spectral radius in a tree is attained by the star graph. In our research, we explore the potential applications of the SDE index in chemical graph theory. Our findings illustrate a noteworthy correlation between the SDE index and several physical and chemical properties. This correlation highlights the promising potential of the index as a predictive tool for the molecular behavior of various compounds. For example, the SDE index has a stronger negative correlation with the M1, M2, and M3 indices (r= −0.93, −0.94, and −0.91, respectively).
Chemical graph theory has made a significant contribution to understand the chemical compound properties in the modern era of chemical science. At present, calculation of the topological indices is ...one of most important area of research in the field of chemical graph theory. Cyclodecane is a cyclic hydrocarbon with the chemical formula
. It consists of a ring of ten carbon atoms bonded together in a cyclical structure. Cyclodecane chains can be part of larger molecules or polymers, where multiple cyclodecane rings are connected together. These molecules can have various applications in chemistry, materials science, and pharmaceuticals. This article aims to determine expected values of some connectivity based topological indices of random cyclodecane chains, containing saturated hydrocarbons with at least two rings. It also compares these descriptors using explicit formulae, numerical tables and present graphical profiles of these comparisons.
The augmented Zagreb index AZI(G) of a connected graph G is defined asAZI(G)=∑uv∈E(G)(d(u)d(v)d(u)+d(v)−2)3, where d(u) and d(v) are the degrees of the end-vertices of an edge uv, respectively. We ...determine the unique tree with given numbers of vertices and leaves that minimizes augmented Zagreb index, and characterize the unique graph with minimum augmented Zagreb index in the class of connected graphs with given numbers of vertices and pendent vertices. Furthermore, we also determine the maximum augmented Zagreb index with the extremal trees characterized in the class of all trees with given numbers of vertices and leaves.
In this paper, we investigate the predictive potential of commonly occurring spectrum-based distance descriptors which are based on eigenvalues of distance-related chemical matrices. For our ...comparative testing, the normal boiling point has been chosen to be representative of van-der-Waals and intermolecular type interactions, whereas, the standard enthalpy/heat of formation is selected to represent thermal properties. We introduce three new chemical matrices and results show that the spectral descriptors based on these new matrices outperform the existing well-studied spectral descriptors. A computational method is used to calculate commonly occurring spectrum-based distance descriptors to investigate their correlation ability with the experimental data for the two chosen physicochemical properties for lower polycyclic aromatic hydrocarbons. By providing the list of the five best spectrum-based distance descriptors, our study contributes towards putting forward the best spectrum-based topological descriptors while mentioning the ones which do not deserve further attention of researchers. Applications of our results to certain families of carbon polyhex nanotubes and one-hexagonal nanocones have been presented. The results can potentially be used to determine certain physicochemical of these nanotubes and nanocones theoretically with higher accuracy and negligible error.
Topological indices are an important method for understanding the fundamental topology of chemical structures. Quantitative structure properties relationship (QSPR) is an analytical approach for ...breaking down a molecule into a sequence of numerical values that describe the chemical and physical characteristics of the molecule. In this article, we have developed the QSPR analysis between eigenvalue‐based topological indices and physical properties of COVID‐19 drugs to predict the significance level of eigenvalue based indices. We have to use MATLAB for the computation of indices and SPSS for analysis. We show that positive interia index, signless Laplacian Estrada index and Randić energy are the best predictors of molar reactivity, polar surface area and molecular weight, respectively.
The topological indices are used to predict the physical properties of chemical compounds. It is an efficient technique in avoiding valuable and long laboratory experiments. For this, we computed the eigenvalue‐based topological indices and developed a quantitative structure–property relationship between these topological indices and the scaling physical properties of COVID‐19 drugs. We have used a MATLAB based algorithm to compute these indices and the correlation between topological indices and physical properties have been developed with the software SPSS. It is found that the positive interia index, signless Laplacian Estrada index and Randić energy possesses the best correlating ability among several topological indices to predict the molar reactivity, polar surface area and molecular weight respectively.
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