Title : ( On the structure of isoclinism classes of the non-commuting graphs )
Authors: Behnaz Tolue , Amin Rafiei , Ahmad Erfanian ,
Full TextAbstract
Abstract In this paper, we introduce the new concept isoclinism of two non-commuting graphs. We describe it with this hope to determine the properties of the graph with large number of vertices and edges more easier by use of its smaller correspondence graph in its isoclinicclass.In1939,Heksterclassifiedthegroupsbyn-isoclinismwhichwasweakerthan isomorphism,wheren isapositiveinteger.Theabeliangroupsareinthesameclassbygroupisoclinism,althoughtheirintrinsicpropertiesarenotthesame.Thenotionofisoclinicgroups is the inspiration to define the isoclinism of two graphs. The isoclinism of two graphs is a pair of significant special isomorphism between the quotient graphs of the given graphs. We observethatallcomplete3-partitenon-commutinggraphsareinthesameisoclinicclassand thenon-commutinggraphassociatedtothedihedralgroupoforder8, D8 istherepresentative of this class.
Keywords
, Isoclinism·Non, commuting graph·Quotient graph
@article{paperid:1071084,
author = {Behnaz Tolue and Amin Rafiei and Erfanian, Ahmad},
title = {On the structure of isoclinism classes of the non-commuting graphs},
journal = {Afrika Matematika},
year = {2018},
volume = {29},
number = {3},
month = {June},
issn = {1012-9405},
pages = {339--348},
numpages = {9},
keywords = {Isoclinism·Non-commuting graph·Quotient graph},
}
%0 Journal Article
%T On the structure of isoclinism classes of the non-commuting graphs
%A Behnaz Tolue
%A Amin Rafiei
%A Erfanian, Ahmad
%J Afrika Matematika
%@ 1012-9405
%D 2018
