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Abstract
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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
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