Seidel Laplacian and Seidel Signless Laplacian energies of commuting graph for dihedral groups
In this paper, we discuss the energy of the commuting graph. The vertex set of the graph is dihedral groups and the edges between two distinct vertices represent the commutativity of the group elements. The spectrum of the graph is associated with the Seidel Laplacian and Seidel signless Laplacian m...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Penerbit UTM Press
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/111692/ http://psasir.upm.edu.my/id/eprint/111692/1/18_3465_%28701-713%29.pdf |
| _version_ | 1848865756401369088 |
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| author | Romdhini, Mamika Ujianita Nawawi, Athirah Syechah, Bulqis Nebula Al-Quran, Ashraf |
| author_facet | Romdhini, Mamika Ujianita Nawawi, Athirah Syechah, Bulqis Nebula Al-Quran, Ashraf |
| author_sort | Romdhini, Mamika Ujianita |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we discuss the energy of the commuting graph. The vertex set of the graph is dihedral groups and the edges between two distinct vertices represent the commutativity of the group elements. The spectrum of the graph is associated with the Seidel Laplacian and Seidel signless Laplacian matrices. The results are similar to the well-known fact that the energies are not odd integers. We also highlight the relation that the Seidel signless Laplacian energy is never less than Seidel Laplacian energy. Ultimately, we classify the graphs according to the energy value as the hyperenergetic. |
| first_indexed | 2025-11-15T14:09:46Z |
| format | Article |
| id | upm-111692 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:09:46Z |
| publishDate | 2024 |
| publisher | Penerbit UTM Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1116922025-02-12T07:24:10Z http://psasir.upm.edu.my/id/eprint/111692/ Seidel Laplacian and Seidel Signless Laplacian energies of commuting graph for dihedral groups Romdhini, Mamika Ujianita Nawawi, Athirah Syechah, Bulqis Nebula Al-Quran, Ashraf In this paper, we discuss the energy of the commuting graph. The vertex set of the graph is dihedral groups and the edges between two distinct vertices represent the commutativity of the group elements. The spectrum of the graph is associated with the Seidel Laplacian and Seidel signless Laplacian matrices. The results are similar to the well-known fact that the energies are not odd integers. We also highlight the relation that the Seidel signless Laplacian energy is never less than Seidel Laplacian energy. Ultimately, we classify the graphs according to the energy value as the hyperenergetic. Penerbit UTM Press 2024-06-26 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/111692/1/18_3465_%28701-713%29.pdf Romdhini, Mamika Ujianita and Nawawi, Athirah and Syechah, Bulqis Nebula and Al-Quran, Ashraf (2024) Seidel Laplacian and Seidel Signless Laplacian energies of commuting graph for dihedral groups. Malaysian Journal of Fundamental and Applied Sciences, 20 (3). pp. 701-713. ISSN 2289-599X https://mjfas.utm.my/index.php/mjfas/article/view/3465 10.11113/mjfas.v20n3.3465 |
| spellingShingle | Romdhini, Mamika Ujianita Nawawi, Athirah Syechah, Bulqis Nebula Al-Quran, Ashraf Seidel Laplacian and Seidel Signless Laplacian energies of commuting graph for dihedral groups |
| title | Seidel Laplacian and Seidel Signless Laplacian energies of commuting graph for dihedral groups |
| title_full | Seidel Laplacian and Seidel Signless Laplacian energies of commuting graph for dihedral groups |
| title_fullStr | Seidel Laplacian and Seidel Signless Laplacian energies of commuting graph for dihedral groups |
| title_full_unstemmed | Seidel Laplacian and Seidel Signless Laplacian energies of commuting graph for dihedral groups |
| title_short | Seidel Laplacian and Seidel Signless Laplacian energies of commuting graph for dihedral groups |
| title_sort | seidel laplacian and seidel signless laplacian energies of commuting graph for dihedral groups |
| url | http://psasir.upm.edu.my/id/eprint/111692/ http://psasir.upm.edu.my/id/eprint/111692/ http://psasir.upm.edu.my/id/eprint/111692/ http://psasir.upm.edu.my/id/eprint/111692/1/18_3465_%28701-713%29.pdf |