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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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Main Authors: Romdhini, Mamika Ujianita, Nawawi, Athirah
Format: Article
Published: University of Malaya 2022
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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spelling 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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description 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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score 13.160551

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