Equal-Square Graphs Associated with Finite Groups

The graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices x and y are adjacent iff x2=y2. We call this graph an equal-square graph of the finite group...

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Main Authors: Shafiq Ur Rehman, Ghulam Farid, Tayaba Tariq, Ebenezer Bonyah
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2022/9244325
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author Shafiq Ur Rehman
Ghulam Farid
Tayaba Tariq
Ebenezer Bonyah
author_facet Shafiq Ur Rehman
Ghulam Farid
Tayaba Tariq
Ebenezer Bonyah
author_sort Shafiq Ur Rehman
collection DOAJ
description The graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices x and y are adjacent iff x2=y2. We call this graph an equal-square graph of the finite group G, symbolized by ESG. Some interesting properties of ESG are studied. Moreover, examples of equal-square graphs of finite cyclic groups, groups of plane symmetries of regular polygons, group of units Un, and the finite abelian groups are constructed.
format Article
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institution Kabale University
issn 2314-4785
language English
publishDate 2022-01-01
publisher Wiley
record_format Article
series Journal of Mathematics
spelling doaj-art-419cca3d2fde4790959783cfc50d04d12025-08-20T03:55:40ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9244325Equal-Square Graphs Associated with Finite GroupsShafiq Ur Rehman0Ghulam Farid1Tayaba Tariq2Ebenezer Bonyah3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Mathematics EducationThe graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices x and y are adjacent iff x2=y2. We call this graph an equal-square graph of the finite group G, symbolized by ESG. Some interesting properties of ESG are studied. Moreover, examples of equal-square graphs of finite cyclic groups, groups of plane symmetries of regular polygons, group of units Un, and the finite abelian groups are constructed.http://dx.doi.org/10.1155/2022/9244325
spellingShingle Shafiq Ur Rehman
Ghulam Farid
Tayaba Tariq
Ebenezer Bonyah
Equal-Square Graphs Associated with Finite Groups
Journal of Mathematics
title Equal-Square Graphs Associated with Finite Groups
title_full Equal-Square Graphs Associated with Finite Groups
title_fullStr Equal-Square Graphs Associated with Finite Groups
title_full_unstemmed Equal-Square Graphs Associated with Finite Groups
title_short Equal-Square Graphs Associated with Finite Groups
title_sort equal square graphs associated with finite groups
url http://dx.doi.org/10.1155/2022/9244325
work_keys_str_mv AT shafiqurrehman equalsquaregraphsassociatedwithfinitegroups
AT ghulamfarid equalsquaregraphsassociatedwithfinitegroups
AT tayabatariq equalsquaregraphsassociatedwithfinitegroups
AT ebenezerbonyah equalsquaregraphsassociatedwithfinitegroups