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.

Symmetric Division Deg Index: Extremal Results and Bounds

“…By the definition of connected r-cyclic graphs, the next result contributes towards the solution to the problem of characterizing graphs attaining the maximum SDD index over the class of all connected r-cyclic molecular graphs of a given order. Here we remark that Theorem 3.18 follows also from a more general result reported recently in [2]. There is no result regarding the minimal version of Theorem 3.19 in the literature.…”

The Euler Sombor index of a graph

“…Lemma 3.11 [19]. Let G be a chemical graph of size m and order n such that n À 1 ≤ m ≤ 2n and n ≥ 13.…”

“…In [19], Albalahi et al addressed the problem of finding graphs with extremum BID indices over the class of all chemical graphs of a fixed number of edges and vertices.…”