A NOTE ON THE COPRIME GRAPH OF A GROUP

Abstract

In this paper we study the coprime graph of a group G. The coprime graph of a group G, denoted by G, is a graph whose vertices are elements of G and two distinct vertices x and y are adjacent if and only if ( jxj;jyj) = 1. In this paper, we show that ( G) = !( G) : We classify all the groups which G is a complete r partite graph or a planar graph. Also we study the automorphism group of G.