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On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups

The non-commuting graph, denoted by , is defined on a finite group , with its vertices are elements of excluding those in the center of . In this graph, two distinct vertices are adjacent whenever they do not commute in . The graph can be associated with several matrices including the most basic m...

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Main Authors: Romdhini, Mamika Ujianita, Nawawi, Athirah
Format: Article
Published: Penerbit UTM Press 2024
Online Access:http://psasir.upm.edu.my/id/eprint/106256/
https://mjfas.utm.my/index.php/mjfas/article/view/3252
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spelling my.upm.eprints.1062562024-06-16T03:09:43Z http://psasir.upm.edu.my/id/eprint/106256/ On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups Romdhini, Mamika Ujianita Nawawi, Athirah The non-commuting graph, denoted by , is defined on a finite group , with its vertices are elements of excluding those in the center of . In this graph, two distinct vertices are adjacent whenever they do not commute in . The graph can be associated with several matrices including the most basic matrix, which is the adjacency matrix, , and a matrix called Sombor matrix, denoted by . The entries of are either the square root of the sum of the squares of degrees of two distinct adjacent vertices, or zero otherwise. Consequently, the adjacency and Sombor energies of is the sum of the absolute eigenvalues of the adjacency and Sombor matrices of , respectively, whereas the spectral radius of is the maximum absolute eigenvalues. Throughout this paper, we find the spectral radius obtained from the spectrum of and the Sombor energy of for dihedral groups of order , where . Moreover, there is an almost linear correlation between the Sombor energy and the adjacency energy of for which is slightly different than reported earlier in previous literature. Penerbit UTM Press 2024 Article PeerReviewed Romdhini, Mamika Ujianita and Nawawi, Athirah (2024) On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups. Malaysian Journal of Fundamental and Applied Sciences, 20 (1). pp. 65-73. ISSN 2289-599X https://mjfas.utm.my/index.php/mjfas/article/view/3252 10.11113/mjfas.v20n1.3252
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 The non-commuting graph, denoted by , is defined on a finite group , with its vertices are elements of excluding those in the center of . In this graph, two distinct vertices are adjacent whenever they do not commute in . The graph can be associated with several matrices including the most basic matrix, which is the adjacency matrix, , and a matrix called Sombor matrix, denoted by . The entries of are either the square root of the sum of the squares of degrees of two distinct adjacent vertices, or zero otherwise. Consequently, the adjacency and Sombor energies of is the sum of the absolute eigenvalues of the adjacency and Sombor matrices of , respectively, whereas the spectral radius of is the maximum absolute eigenvalues. Throughout this paper, we find the spectral radius obtained from the spectrum of and the Sombor energy of for dihedral groups of order , where . Moreover, there is an almost linear correlation between the Sombor energy and the adjacency energy of for which is slightly different than reported earlier in previous literature.
format Article
author Romdhini, Mamika Ujianita
Nawawi, Athirah
spellingShingle Romdhini, Mamika Ujianita
Nawawi, Athirah
On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups
author_facet Romdhini, Mamika Ujianita
Nawawi, Athirah
author_sort Romdhini, Mamika Ujianita
title On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups
title_short On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups
title_full On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups
title_fullStr On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups
title_full_unstemmed On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups
title_sort on the spectral radius and sombor energy of the non-commuting graph for dihedral groups
publisher Penerbit UTM Press
publishDate 2024
url http://psasir.upm.edu.my/id/eprint/106256/
https://mjfas.utm.my/index.php/mjfas/article/view/3252
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score 13.244368

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