Analysis of Complex Networks via Some Novel Topological Indices

Abstract

Chemical graph theory is a field of mathematical chemistry that links mathematics, chemistry, and graph theory to solve chemistry-related issues quantitatively. Mathematical chemistry is an area of mathematics that employs mathematical methods to tackle chemical-related problems. A graphical representation of chemical molecules, known as the molecular graph of the chemical substance, is one of these tools. A topological index (TI) is a mathematical function that assigns a numerical value to a (molecular) graph and predicts many physical, chemical, biological, thermodynamical, and structural features of that network. In this work, we calculate a new topological index namely, the Sombor index, the Super Sombor index, and its reduced version for chemical networks. We also plot our computed results to examine how they were affected by the parameters involved. This document lists the distinct degrees and degree sums of enhanced mesh network, triangular mesh network, star of silicate network, and rhenium trioxide lattice. The edge partitions of these families of networks are tabled which depend on the sum of degrees of end vertices and the sum of the degree-based edges. These edge partitions are used to find closed formulae for numerous degree-based topological indices of the networks.