Maximum and minimum degree energy of commuting graph for dihedral groups
If is a finite group and is the centre of , then the commuting graph for , denoted by , has as its vertices set with two distinct vertices and are adjacent if . The degree of the vertex of , denoted by , is the number of vertices adjacent to . The maximum (or minimum) degree matrix...
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| Format: | Article |
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Penerbit UKM
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/102147/ |
| _version_ | 1848863727155150848 |
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| author | Romdhini, Mamika Ujianita Nawawi, Athirah |
| author_facet | Romdhini, Mamika Ujianita Nawawi, Athirah |
| author_sort | Romdhini, Mamika Ujianita |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | If is a finite group and is the centre of , then the commuting graph for , denoted by , has as its vertices set with two distinct vertices and are adjacent if . The degree of the vertex of , denoted by , is the number of vertices adjacent to . The maximum (or minimum) degree matrix of is a square matrix whose -th entry is whenever and are adjacent, otherwise, it is zero. This study presents the maximum and minimum degree energies of for dihedral groups of order , by using the absolute eigenvalues of the corresponding maximum degree matrices ( ) and minimum degree matrices ( ).Here, the comparison of maximum and minimum degree energy of for is discussed by considering odd and even cases. The result shows that for each case, both energies are non-negative even integers and always equal. |
| first_indexed | 2025-11-15T13:37:31Z |
| format | Article |
| id | upm-102147 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:37:31Z |
| publishDate | 2022 |
| publisher | Penerbit UKM |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1021472024-01-16T03:56:22Z http://psasir.upm.edu.my/id/eprint/102147/ Maximum and minimum degree energy of commuting graph for dihedral groups Romdhini, Mamika Ujianita Nawawi, Athirah If is a finite group and is the centre of , then the commuting graph for , denoted by , has as its vertices set with two distinct vertices and are adjacent if . The degree of the vertex of , denoted by , is the number of vertices adjacent to . The maximum (or minimum) degree matrix of is a square matrix whose -th entry is whenever and are adjacent, otherwise, it is zero. This study presents the maximum and minimum degree energies of for dihedral groups of order , by using the absolute eigenvalues of the corresponding maximum degree matrices ( ) and minimum degree matrices ( ).Here, the comparison of maximum and minimum degree energy of for is discussed by considering odd and even cases. The result shows that for each case, both energies are non-negative even integers and always equal. Penerbit UKM 2022 Article PeerReviewed Romdhini, Mamika Ujianita and Nawawi, Athirah (2022) Maximum and minimum degree energy of commuting graph for dihedral groups. Sains Malaysiana, 51 (12). pp. 4145-4151. ISSN 0126-6039 https://www.ukm.my/jsm/english_journals/vol51num12_2022/vol51num12_2022pg4145-4151.html 10.17576/jsm-2022-5112-21 |
| spellingShingle | Romdhini, Mamika Ujianita Nawawi, Athirah Maximum and minimum degree energy of commuting graph for dihedral groups |
| title | Maximum and minimum degree energy of commuting graph for dihedral groups |
| title_full | Maximum and minimum degree energy of commuting graph for dihedral groups |
| title_fullStr | Maximum and minimum degree energy of commuting graph for dihedral groups |
| title_full_unstemmed | Maximum and minimum degree energy of commuting graph for dihedral groups |
| title_short | Maximum and minimum degree energy of commuting graph for dihedral groups |
| title_sort | maximum and minimum degree energy of commuting graph for dihedral groups |
| url | http://psasir.upm.edu.my/id/eprint/102147/ http://psasir.upm.edu.my/id/eprint/102147/ http://psasir.upm.edu.my/id/eprint/102147/ |