On Bond Incident Degree Indices of Chemical Graphs

Abstract

By swapping out atoms for vertices and bonds for edges, a graph may be used to model any molecular structure. A graph G is considered to be a chemical graph in graph theory if no vertex of G has a degree of 5 or greater. The bond incident degree (BID) index for a chemical graph G is defined as the total of contributions f(dG(u),dG(v)) from all edges uv of G, where dG(w) stands for the degree of a vertex w of G, E(G) is the set of edges of G, and f is a real-valued symmetric function. This paper addresses the problem of finding graphs with extremum BID indices over the class of all chemical graphs of a fixed number of edges and vertices.