Abstract
Abstract - Let G be a non- abelian finite group. The non-commuting graph ,is defined as a graph with a vertex set − G-Z(G)in which two vertices x and y are joined if and only if xy ≠ yx. In this paper, we invest some results on the number of edges set , the degree of avertex of non-commuting graph and the number of conjugacy classes of a finite group. In order that if non-commuting graph of H ≅ non - commuting graph of G,H is afinite group, then |G| = |H| .
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