Citation
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
Abstract
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.
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science Institute for Mathematical Research |
| DOI Number: | https://doi.org/10.47836/mjms.17.1.05 |
| Publisher: | Universiti Putra Malaysia |
| Keywords: | Commuting graph; Non-commuting graph; Dihedral group; Neighbors degree sum matrix; The energy of a graph; Quality education |
| Depositing User: | Ms. Che Wa Zakaria |
| Date Deposited: | 11 Oct 2024 07:47 |
| Last Modified: | 11 Oct 2024 07:47 |
| Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.47836/mjms.17.1.05 |
| URI: | http://psasir.upm.edu.my/id/eprint/108548 |
| Statistic Details: | View Download Statistic |
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