University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 25 4 2014 12 01 A Kind of Non-commuting Graph of Finite Groups 379 384 52625 EN B. Tolue 1Department of Pure Mathematics, Faculty of Sciences, Hakim Sabzevari University, Sabzevar, Islamic republic of Iran A. Erfanian 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. A. Jafarzadeh 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. Journal Article 2013 10 28 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. https://jsciences.ut.ac.ir/article_52625_d10ebf26020ddfc9803c7628524add3d.pdf