University of TehranJournal of Sciences, Islamic Republic of Iran1016-110425420141201A Kind of Non-commuting Graph of Finite Groups37938452625ENB.Tolue1Department of Pure Mathematics, Faculty of Sciences, Hakim Sabzevari University, Sabzevar, Islamic republic of IranA.Erfanian2 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.Jafarzadeh2 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 Article20131028Let 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