hamidreza dorbidi

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