Title : ( A Kind of Non-commuting Graph of Finite Groups )
Authors: B. Tolue , Ahmad Erfanian , Abbas Jafarzadeh ,
Full TextAbstract
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 Γ _g, G. 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.
Keywords
, g, noncommuting graph; commutator; non, commuting graph; isoclinism
@article{paperid:1047068,
author = {B. Tolue and Erfanian, Ahmad and Jafarzadeh, Abbas},
title = {A Kind of Non-commuting Graph of Finite Groups},
journal = {Journal of Sciences, Islamic Republic of Iran},
year = {2014},
volume = {25},
number = {4},
month = {March},
issn = {1016-1104},
pages = {379--384},
numpages = {5},
keywords = {g-noncommuting graph; commutator; non-commuting graph; isoclinism},
}
%0 Journal Article
%T A Kind of Non-commuting Graph of Finite Groups
%A B. Tolue
%A Erfanian, Ahmad
%A Jafarzadeh, Abbas
%J Journal of Sciences, Islamic Republic of Iran
%@ 1016-1104
%D 2014
