1
1Department of Pure Mathematics, Faculty of Sciences, Hakim Sabzevari University, Sabzevar, Islamic republic of Iran
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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.
Abstract
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.
Tolue,B , Erfanian,A and Jafarzadeh,A . (2014). A Kind of Non-commuting Graph of Finite Groups. Journal of Sciences, Islamic Republic of Iran, 25(4), 379-384.
MLA
Tolue,B , , Erfanian,A , and Jafarzadeh,A . "A Kind of Non-commuting Graph of Finite Groups", Journal of Sciences, Islamic Republic of Iran, 25, 4, 2014, 379-384.
HARVARD
Tolue B, Erfanian A, Jafarzadeh A. (2014). 'A Kind of Non-commuting Graph of Finite Groups', Journal of Sciences, Islamic Republic of Iran, 25(4), pp. 379-384.
CHICAGO
B Tolue, A Erfanian and A Jafarzadeh, "A Kind of Non-commuting Graph of Finite Groups," Journal of Sciences, Islamic Republic of Iran, 25 4 (2014): 379-384,
VANCOUVER
Tolue B, Erfanian A, Jafarzadeh A. A Kind of Non-commuting Graph of Finite Groups. J. Sci. I. R. I.. 2014;25(4):379-384.
Journal of Sciences, Islamic Republic of Iran