%0 Journal Article %T A Kind of Non-commuting Graph of Finite Groups %J Journal of Sciences, Islamic Republic of Iran %I University of Tehran %Z 1016-1104 %A Tolue, B. %A Erfanian, A. %A Jafarzadeh, A. %D 2014 %\ 12/01/2014 %V 25 %N 4 %P 379-384 %! A Kind of Non-commuting Graph of Finite Groups %K g-noncommuting graph %K commutator %K non-commuting graph %K isoclinism %R %X 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. %U https://jsciences.ut.ac.ir/article_52625_d10ebf26020ddfc9803c7628524add3d.pdf