Energy and Laplacian energy of the relative co-prime graph for symmetric group of order six
The energy of a graph is calculated as the sum of the modulus of eigenvalues of an adjacency matrix for a graph. The Laplacian energy refers to the eigenvalues of the graph’s Laplacian matrix. In graph theory, the co-prime graph of a group is a graph where the vertices represent the elements of a gr...
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Penerbit Universiti Kebangsaan Malaysia
2025
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| Online Access: | http://journalarticle.ukm.my/26340/1/Paper_6%20-.pdf http://journalarticle.ukm.my/26340/ https://www.ukm.my/jqma/ |
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| author | Norarida Abd Rhani, Muhammad Alif Haikal Mokhtar, Nur Zurin Iwani Hashim, Fadila Normahia Abd Manaf, Muhanizah Abdul Hamid, |
| author_facet | Norarida Abd Rhani, Muhammad Alif Haikal Mokhtar, Nur Zurin Iwani Hashim, Fadila Normahia Abd Manaf, Muhanizah Abdul Hamid, |
| author_sort | Norarida Abd Rhani, |
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| content_provider | Universiti Kebangsaan Malaysia |
| content_source | UKM Journal Article Repository |
| continent | Asia |
| country | Malaysia |
| description | The energy of a graph is calculated as the sum of the modulus of eigenvalues of an adjacency matrix for a graph. The Laplacian energy refers to the eigenvalues of the graph’s Laplacian matrix. In graph theory, the co-prime graph of a group is a graph where the vertices represent the elements of a group, and two distinct vertices are connected if and only if their orders are relatively prime. This study is then extended to the relative co-prime graph of a group, where the vertices are the elements of the group, and two distinct vertices are adjacent if and only if their orders are co-prime and any of them is in the subgroup. By using the definition of the relative co-prime graph of a group with respect to a subgroup, some graphs of symmetric group of order six are constructed. Some energies and Laplacian energies of the relative co-prime graph related to the symmetric group of order six are also obtained. |
| format | Article |
| id | my-ukm.journal.26340 |
| institution | Universiti Kebangsaan Malaysia |
| language | en |
| publishDate | 2025 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| record_format | eprints |
| spelling | my-ukm.journal.263402026-01-09T06:41:11Z http://journalarticle.ukm.my/26340/ Energy and Laplacian energy of the relative co-prime graph for symmetric group of order six Norarida Abd Rhani, Muhammad Alif Haikal Mokhtar, Nur Zurin Iwani Hashim, Fadila Normahia Abd Manaf, Muhanizah Abdul Hamid, The energy of a graph is calculated as the sum of the modulus of eigenvalues of an adjacency matrix for a graph. The Laplacian energy refers to the eigenvalues of the graph’s Laplacian matrix. In graph theory, the co-prime graph of a group is a graph where the vertices represent the elements of a group, and two distinct vertices are connected if and only if their orders are relatively prime. This study is then extended to the relative co-prime graph of a group, where the vertices are the elements of the group, and two distinct vertices are adjacent if and only if their orders are co-prime and any of them is in the subgroup. By using the definition of the relative co-prime graph of a group with respect to a subgroup, some graphs of symmetric group of order six are constructed. Some energies and Laplacian energies of the relative co-prime graph related to the symmetric group of order six are also obtained. Penerbit Universiti Kebangsaan Malaysia 2025-06 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/26340/1/Paper_6%20-.pdf Norarida Abd Rhani, and Muhammad Alif Haikal Mokhtar, and Nur Zurin Iwani Hashim, and Fadila Normahia Abd Manaf, and Muhanizah Abdul Hamid, (2025) Energy and Laplacian energy of the relative co-prime graph for symmetric group of order six. Journal of Quality Measurement and Analysis, 21 (2). pp. 69-77. ISSN 2600-8602 https://www.ukm.my/jqma/ |
| spellingShingle | Norarida Abd Rhani, Muhammad Alif Haikal Mokhtar, Nur Zurin Iwani Hashim, Fadila Normahia Abd Manaf, Muhanizah Abdul Hamid, Energy and Laplacian energy of the relative co-prime graph for symmetric group of order six |
| title | Energy and Laplacian energy of the relative co-prime graph for symmetric group of order six |
| title_full | Energy and Laplacian energy of the relative co-prime graph for symmetric group of order six |
| title_fullStr | Energy and Laplacian energy of the relative co-prime graph for symmetric group of order six |
| title_full_unstemmed | Energy and Laplacian energy of the relative co-prime graph for symmetric group of order six |
| title_short | Energy and Laplacian energy of the relative co-prime graph for symmetric group of order six |
| title_sort | energy and laplacian energy of the relative co-prime graph for symmetric group of order six |
| url | http://journalarticle.ukm.my/26340/1/Paper_6%20-.pdf http://journalarticle.ukm.my/26340/ https://www.ukm.my/jqma/ |
| url_provider | http://journalarticle.ukm.my/ |