Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups

The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas...

Full description

Bibliographic Details
Main Authors: Romdhini, M. U., Nawawi, A., Chen, C. Y.
Format: Article
Language:English
Published: Universiti Putra Malaysia 2023
Online Access:http://psasir.upm.edu.my/id/eprint/108548/
http://psasir.upm.edu.my/id/eprint/108548/1/Neighbors%20Degree%20Sum%20Energy.pdf
_version_ 1848865170722390016
author Romdhini, M. U.
Nawawi, A.
Chen, C. Y.
author_facet Romdhini, M. U.
Nawawi, A.
Chen, C. Y.
author_sort Romdhini, M. U.
building UPM Institutional Repository
collection Online Access
description The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas for the diagonal entries are the negative of the square of vertex degree. This study presents the formulas of neighbors degree sum energies of commuting and non-commuting graphs for dihedral groups of order 2n, D2n, for two cases−odd and even n. The results in this paper comply with the well known fact that energy of a graph is neither an odd integer nor a square root of an odd integer.
first_indexed 2025-11-15T14:00:27Z
format Article
id upm-108548
institution Universiti Putra Malaysia
institution_category Local University
language English
last_indexed 2025-11-15T14:00:27Z
publishDate 2023
publisher Universiti Putra Malaysia
recordtype eprints
repository_type Digital Repository
spelling upm-1085482024-10-11T07:47:17Z http://psasir.upm.edu.my/id/eprint/108548/ Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups Romdhini, M. U. Nawawi, A. Chen, C. Y. The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas for the diagonal entries are the negative of the square of vertex degree. This study presents the formulas of neighbors degree sum energies of commuting and non-commuting graphs for dihedral groups of order 2n, D2n, for two cases−odd and even n. The results in this paper comply with the well known fact that energy of a graph is neither an odd integer nor a square root of an odd integer. Universiti Putra Malaysia 2023-03-27 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/108548/1/Neighbors%20Degree%20Sum%20Energy.pdf Romdhini, M. U. and Nawawi, A. and Chen, C. Y. (2023) Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups. Malaysian Journal of Mathematical Sciences, 17 (1). pp. 53-65. ISSN 1823-8343; ESSN: 2289-750X https://mjms.upm.edu.my/lihatmakalah.php?kod=2023/March/17/1/53-65 10.47836/mjms.17.1.05
spellingShingle Romdhini, M. U.
Nawawi, A.
Chen, C. Y.
Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups
title Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups
title_full Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups
title_fullStr Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups
title_full_unstemmed Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups
title_short Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups
title_sort neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups
url http://psasir.upm.edu.my/id/eprint/108548/
http://psasir.upm.edu.my/id/eprint/108548/
http://psasir.upm.edu.my/id/eprint/108548/
http://psasir.upm.edu.my/id/eprint/108548/1/Neighbors%20Degree%20Sum%20Energy.pdf