TY - JOUR ID - 52625 TI - A Kind of Non-commuting Graph of Finite Groups JO - Journal of Sciences, Islamic Republic of Iran JA - JSCIENCES LA - en SN - 1016-1104 AU - Tolue, B. AU - Erfanian, A. AU - Jafarzadeh, A. AD - 1Department of Pure Mathematics, Faculty of Sciences, Hakim Sabzevari University, Sabzevar, Islamic republic of Iran AD - 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. Y1 - 2014 PY - 2014 VL - 25 IS - 4 SP - 379 EP - 384 KW - g-noncommuting graph KW - commutator KW - non-commuting graph KW - isoclinism DO - N2 - 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. UR - https://jsciences.ut.ac.ir/article_52625.html L1 - https://jsciences.ut.ac.ir/article_52625_d10ebf26020ddfc9803c7628524add3d.pdf ER -