Comptes Rendus de L Academie Bulgare des Sciences, ( ISI ), Volume (67), No (8), Year (2014-8) , Pages (1037-1044)

Title : ( The Generalised Non-Commuting Gragh OF A Finite Group )

Authors: Somayeh Ghayekhloo , Ahmad Erfanian , Behnaz Tolue ,

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In this paper we define the generalised non-commuting graph Γ(H,K) , where H and K are two subgroups of a non-abelian group G. Take (H ∪ K) \ (CH(K) ∪ CK(H)) as the vertices of the graph and two distinct vertices x and y join, whenever x or y is in H and [x, y] 6= 1. We obtain diameter and girth of this graph. Also, we discuss the dominating set and planarity of Γ(H,K) . Moreover, we try to find a connection between Γ(H,K) and the relative commutativity degree of two subgroups d(H, K). Furthermore, we prove that if Γ(H,G) ∼= Γ(K,G) , then ΓH ∼= ΓK. And finally we introduce a special case when subgroup K is equal to the non-abelian group G.

Keywords

, commutativity degree, non-abelian group, non-commuting
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@article{paperid:1059862,
author = {Ghayekhloo, Somayeh and Erfanian, Ahmad and Behnaz Tolue},
title = {The Generalised Non-Commuting Gragh OF A Finite Group},
journal = {Comptes Rendus de L Academie Bulgare des Sciences},
year = {2014},
volume = {67},
number = {8},
month = {August},
issn = {1310-1331},
pages = {1037--1044},
numpages = {7},
keywords = {commutativity degree; non-abelian group; non-commuting graph},
}

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%0 Journal Article
%T The Generalised Non-Commuting Gragh OF A Finite Group
%A Ghayekhloo, Somayeh
%A Erfanian, Ahmad
%A Behnaz Tolue
%J Comptes Rendus de L Academie Bulgare des Sciences
%@ 1310-1331
%D 2014

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