| Issue |
RAIRO-Oper. Res.
Volume 58, Number 4, July-August 2024
|
|
|---|---|---|
| Page(s) | 2845 - 2864 | |
| DOI | https://doi.org/10.1051/ro/2024111 | |
| Published online | 15 July 2024 | |
Spectral properties of Sombor matrix of threshold graphs
1
Department of Mathematical Sciences, College of Science, United Arab Emirate University, Al Ain 15551, UAE
2
Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, UAE
3
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
* Corresponding author: bilalahmadrr@gmail.com
Received:
10
January
2024
Accepted:
10
May
2024
We investigate the Sombor spectral properties of threshold graphs, a formula for the Sombor index is presented, the Sombor eigenvalues are given, graphs with simple Sombor eigenvalues are characterized, bounds on the smallest/largest Sombor eigenvalues are presented, the multiplicities of the Sombor eigenvalues are discussed, formulae for trace and determinant of the associated quotient matrix are given, the Sombor spread bound and the bounds on the Sombor energy along with the characterization of extremal graphs. At the end, the conclusion states that all our results are valid for adjacency matrix and other adjacency type matrices.
Mathematics Subject Classification: 05C50 / 15A18
Key words: Adjacency matrix / Sombor matrix / quotient matrix / Sombor eigenvalues / Sombor energy / threshold graphs
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
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