On spectrum and energy of identity graph for group of integers modulo n, Zn
Groups and graphs are two concepts of algebraic mathematics. This paper focuses on group structures that can be expressed in graphs known as identity graphs. We investigate the energy of the identity graph for a group of integers modulo n, Zn, for odd and even n corresponding to adjacency, Laplacian...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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New York Business Global
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/115985/ http://psasir.upm.edu.my/id/eprint/115985/1/115985.pdf |
| _version_ | 1848866905983549440 |
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| author | Romdhini, Mamika Ujianita Nawawi, Athirah Al-Sharqi, Faisal Salwa |
| author_facet | Romdhini, Mamika Ujianita Nawawi, Athirah Al-Sharqi, Faisal Salwa |
| author_sort | Romdhini, Mamika Ujianita |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Groups and graphs are two concepts of algebraic mathematics. This paper focuses on group structures that can be expressed in graphs known as identity graphs. We investigate the energy of the identity graph for a group of integers modulo n, Zn, for odd and even n corresponding to adjacency, Laplacian, and signless Laplacian matrices. It can be seen that the Laplacian and signless Laplacian energies are always equal and are always an even integer. Meanwhile, the adjacency energy is never an odd integer for n is odd. |
| first_indexed | 2025-11-15T14:28:02Z |
| format | Article |
| id | upm-115985 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:28:02Z |
| publishDate | 2024 |
| publisher | New York Business Global |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1159852025-03-19T06:52:39Z http://psasir.upm.edu.my/id/eprint/115985/ On spectrum and energy of identity graph for group of integers modulo n, Zn Romdhini, Mamika Ujianita Nawawi, Athirah Al-Sharqi, Faisal Salwa Groups and graphs are two concepts of algebraic mathematics. This paper focuses on group structures that can be expressed in graphs known as identity graphs. We investigate the energy of the identity graph for a group of integers modulo n, Zn, for odd and even n corresponding to adjacency, Laplacian, and signless Laplacian matrices. It can be seen that the Laplacian and signless Laplacian energies are always equal and are always an even integer. Meanwhile, the adjacency energy is never an odd integer for n is odd. New York Business Global 2024 Article PeerReviewed text en cc_by_nc_4 http://psasir.upm.edu.my/id/eprint/115985/1/115985.pdf Romdhini, Mamika Ujianita and Nawawi, Athirah and Al-Sharqi, Faisal and Salwa (2024) On spectrum and energy of identity graph for group of integers modulo n, Zn. European Journal of Pure and Applied Mathematics, 17 (4). pp. 2915-2929. ISSN 1307-5543 https://www.ejpam.com/index.php/ejpam/article/view/5375 10.29020/nybg.ejpam.v17i4.5375 |
| spellingShingle | Romdhini, Mamika Ujianita Nawawi, Athirah Al-Sharqi, Faisal Salwa On spectrum and energy of identity graph for group of integers modulo n, Zn |
| title | On spectrum and energy of identity graph for group of integers modulo n, Zn |
| title_full | On spectrum and energy of identity graph for group of integers modulo n, Zn |
| title_fullStr | On spectrum and energy of identity graph for group of integers modulo n, Zn |
| title_full_unstemmed | On spectrum and energy of identity graph for group of integers modulo n, Zn |
| title_short | On spectrum and energy of identity graph for group of integers modulo n, Zn |
| title_sort | on spectrum and energy of identity graph for group of integers modulo n, zn |
| url | http://psasir.upm.edu.my/id/eprint/115985/ http://psasir.upm.edu.my/id/eprint/115985/ http://psasir.upm.edu.my/id/eprint/115985/ http://psasir.upm.edu.my/id/eprint/115985/1/115985.pdf |