Editorial: Topological investigations of chemical networks

Muhammad Javaid,Muhammad Imran

doi:10.1515/mgmc-2021-0030

Abstract

Abstract The topic of computing the topological indices (TIs) being a graph-theoretic modeling of the networks or discrete structures has become an important area of research nowadays because of its immense applications in various branches of the applied sciences. TIs have played a vital role in mathematical chemistry since the pioneering work of famous chemist Harry Wiener in 1947. However, in recent years, their capability and popularity has increased significantly because of the findings of the different physical and chemical investigations in the various chemical networks and the structures arising from the drug designs. In additions, TIs are also frequently used to study the quantitative structure property relationships (QSPRs) and quantitative structure activity relationships (QSARs) models which correlate the chemical structures with their physio-chemical properties and biological activities in a dataset of chemicals. These models are very important and useful for the research community working in the wider area of cheminformatics which is an interdisciplinary field combining mathematics, chemistry, and information science. The aim of this editorial is to arrange new methods, techniques, models, and algorithms to study the various theoretical and computational aspects of the different types of these topological indices for the various molecular structures.

Highlights

Introduction and preliminariesFor a finite nonempty set V, a graph G(V; E) being a pair of two sets V and E ⊆ V × V can be visualized by representing the elements of V by nodes or vertices and joining an unordered pair of vertices (u; v) by a bond or edge if and only if (u; v) ∈ E(G) (Harary, 1969)
Latter the same was proclaimed as Wiener index. Afterwards, this area has flourished with a large number of new kind of topological indices (TIs) and many researchers have developed in terms of connectivity, eccentricity, degree, and distance based aspects of a molecular graph which atoms are regarded as nodes/vertices and bonds between them are shown by edges
A bunch of topological descriptors based on aforesaid properties of graphs are classic Zagrab indices developed by Gutman and Trinajstic (1972) widely known as first and second Zagreb indices

Summary

Introduction

Introduction and preliminariesFor a finite nonempty set V, a graph G(V; E) being a pair of two sets V and E ⊆ V × V can be visualized by representing the elements of V by nodes or vertices and joining an unordered pair of vertices (u; v) by a bond or edge if and only if (u; v) ∈ E(G) (Harary, 1969). The aim of this editorial is to arrange new methods, techniques, models, and algorithms to study the various theoretical and computational aspects of the different types of these topological indices for the various molecular structures. A chemical graph is said to be a molecular graph if the degree of each vertex is less than four.

Results

Conclusion