Document Type : Original Paper


1 1Department of Pure Mathematics, Faculty of Sciences, Hakim Sabzevari University, Sabzevar, Islamic republic of Iran

2 2 Department of Mathematics and Center of Excellence in Analysis on Algebraic Structures, Faculty of Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic republic of Iran.


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.