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: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9244325 |
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| _version_ | 1849304647954595840 |
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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 |
| id | doaj-art-419cca3d2fde4790959783cfc50d04d1 |
| 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 |