Degree sum energy of non-commuting graph for dihedral groups
For a finite group G, let Z(G) be the centre of G. Then the non-commuting graph on G, denoted by ΓG, has G\Z(G) as its vertex set with two distinct vertices vp and vq joined by an edge whenever vpvq ≠ vqvp. The degree sum matrix of a graph is a square matrix whose (p,q)-th entry is dvp + dvq wheneve...
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University of Malaya
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/100884/ https://mjs.um.edu.my/index.php/MJS/article/view/34834 |
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my.upm.eprints.1008842023-07-26T03:02:46Z http://psasir.upm.edu.my/id/eprint/100884/ Degree sum energy of non-commuting graph for dihedral groups Romdhini, Mamika Ujianita Nawawi, Athirah For a finite group G, let Z(G) be the centre of G. Then the non-commuting graph on G, denoted by ΓG, has G\Z(G) as its vertex set with two distinct vertices vp and vq joined by an edge whenever vpvq ≠ vqvp. The degree sum matrix of a graph is a square matrix whose (p,q)-th entry is dvp + dvq whenever p is different from q, otherwise, it is zero, where dvi is the degree of the vertex vi. This study presents the general formula for the degree sum energy, EDS (ΓG), for the non-commuting graph of dihedral groups of order 2n, D2n, for all n ≥ 3. University of Malaya 2022-09 Article PeerReviewed Romdhini, Mamika Ujianita and Nawawi, Athirah (2022) Degree sum energy of non-commuting graph for dihedral groups. Malaysian Journal of Science, 41. 34 - 39. ISSN 1394-3065 https://mjs.um.edu.my/index.php/MJS/article/view/34834 10.22452/mjs.sp2022no.1.5 |
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For a finite group G, let Z(G) be the centre of G. Then the non-commuting graph on G, denoted by ΓG, has G\Z(G) as its vertex set with two distinct vertices vp and vq joined by an edge whenever vpvq ≠ vqvp. The degree sum matrix of a graph is a square matrix whose (p,q)-th entry is dvp + dvq whenever p is different from q, otherwise, it is zero, where dvi is the degree of the vertex vi. This study presents the general formula for the degree sum energy, EDS (ΓG), for the non-commuting graph of dihedral groups of order 2n, D2n, for all n ≥ 3. |
| format |
Article |
| author |
Romdhini, Mamika Ujianita Nawawi, Athirah |
| spellingShingle |
Romdhini, Mamika Ujianita Nawawi, Athirah Degree sum energy of non-commuting graph for dihedral groups |
| author_facet |
Romdhini, Mamika Ujianita Nawawi, Athirah |
| author_sort |
Romdhini, Mamika Ujianita |
| title |
Degree sum energy of non-commuting graph for dihedral groups |
| title_short |
Degree sum energy of non-commuting graph for dihedral groups |
| title_full |
Degree sum energy of non-commuting graph for dihedral groups |
| title_fullStr |
Degree sum energy of non-commuting graph for dihedral groups |
| title_full_unstemmed |
Degree sum energy of non-commuting graph for dihedral groups |
| title_sort |
degree sum energy of non-commuting graph for dihedral groups |
| publisher |
University of Malaya |
| publishDate |
2022 |
| url |
http://psasir.upm.edu.my/id/eprint/100884/ https://mjs.um.edu.my/index.php/MJS/article/view/34834 |
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