Several topological indices and entropies for certain families of commutative graphs over Quaternion groups

A group graph is a type of graph formed by combining a group, usually a finite group, with a generating set for that group. Group graphs are employed in various mathematical situations, including algebraic and computational group theory. A graph G is known as a commutative graph if the vertex set of G is a group and two elements are adjacent to each other if they are commuting to each other. In this work, we consider the family of commutative graphs over Quaternion groups. The edge partition mappings related to the degree of each vertex of the graph G are computed. Further, we established many results on various kinds of topological indices and entropies by using M-polynomials. The numerical comparison among computed topological indices has been proposed.