SOME REMARKS ON THE ORDER SUPERGRAPH OF THE POWER GRAPH OF A FINITE GROUP

Abstract

Let G be a finite group. The main supergraph S(G) is a graphwith vertex set G in which two vertices x and y are adjacent if and only ifo(x)|o(y) or o(y)|o(x). In an earlier paper, the main properties of this graphwas obtained. The aim of this paper is to investigate the Hamiltonianity,Eulerianness and 2-connectedness of this graph.