ScienceAsia, ( ISI ), Volume (42), No (3), Year (2016-6) , Pages (231-235)

Title : ( Generalization of the non-commuting graph of a group via a normal subgroup )

Authors: fereshteh kakeri , Ahmad Erfanian , farzaneh mansoori ,

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ABSTRACT: Let G be a finite group and N be a normal subgroup of G. We define an undirected simple graph N,G to be a graph whose vertex set is all elements in G n ZN (G) and two vertices x and y are adjacent iff [x, y] = 2 N, where ZN (G) = fg 2 G : [x, g] 2 N for all x 2 Gg. If N = 1, then we obtain the known non-commuting graph of G. We give some basic results about connectivity, regularity, planarity, 1-planarity and some numerical invariants of the graph which are mostly improvements of the results given for non-commuting graphs. Also, a probability related to this graph is defined and a formula for the number of edges of the graph in terms of this probability is given.

Keywords

, commutativity degree, graph diameter, girth, strongly regular, planar
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@article{paperid:1058358,
author = {Kakeri, Fereshteh and Erfanian, Ahmad and Mansoori, Farzaneh},
title = {Generalization of the non-commuting graph of a group via a normal subgroup},
journal = {ScienceAsia},
year = {2016},
volume = {42},
number = {3},
month = {June},
issn = {1513-1874},
pages = {231--235},
numpages = {4},
keywords = {commutativity degree; graph diameter; girth; strongly regular; planar graph},
}

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%0 Journal Article
%T Generalization of the non-commuting graph of a group via a normal subgroup
%A Kakeri, Fereshteh
%A Erfanian, Ahmad
%A Mansoori, Farzaneh
%J ScienceAsia
%@ 1513-1874
%D 2016

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