Topological Indices of the Non-commuting Graph for Generalised Quaternion Group

Abstract

A topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties and chemical reactivity. It is calculated from a graph representing a molecule. Meanwhile, the non-commuting graph, $$\Gamma _G$$ of G, is defined as a graph of vertex set whose vertices are non-central elements and two distinct vertices are joined by an edge if and only if they do not commute. The main objective of this article is to determine the general formula of some topological indices, namely Wiener index, first Zagreb index and second Zagreb index for the non-commuting graph associated with generalised quaternion group in terms of n.