Hamid Reza Dorbidi - Department of Basic Sciences, University of Jiroft, Jiroft, Kerman, Iran

‎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|)=۱‎. ‎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.

coprime graph, Planner graph, automorphism group