On Structure of Order Graphs Arising from Groups
Avinash J. Kamble, Ravindra P. Rewaskar · Annals of Pure and Applied Mathematics · 2020
Graph theory is a helpful tool in studying group properties. There has been a strong relationship between group (finite group) and graph theories for more than a century. The order graph of a finite group is the graph (undirected) whose vertices are the elements of the group and for any two distinct vertices H and K there is an edge from H to K , if and only if, order of H divides order of K (or vice-versa). In this paper, we focus on the interplay between the group-theoretic properties of G (finite group) and the graph-theoretic properties of Γ(G)(undirected graph).