A Kind of Non-commuting Graph of Finite Groups

Let g be a fixed element of a finite group g. we introduce the g-noncommuting graph of g whose vertex set is whole elements of the group g and two vertices x,y are adjacent whenever [x,y] g and [y,x] g. we denote this graph by . in this paper, we present some graph theoretical properties of g-noncommuting graph. specially, we investigate about its planarity and regularity, its clique number and dominating number. we prove that if g, h are isoclinic groups with |z (g)|=|z (h)|, then their associated graphs are isomorphic.