Sombor spectra of chain graphs

Muhammad Imran; Bilal Ahmad Rather

doi:10.1016/j.heliyon.2023.e18135

Sombor spectra of chain graphs

Heliyon. 2023 Jul 13;9(7):e18135. doi: 10.1016/j.heliyon.2023.e18135. eCollection 2023 Jul.

Authors

Muhammad Imran¹, Bilal Ahmad Rather¹

Affiliation

¹ Mathematical Sciences Department, College of Science, United Arab Emirate University, Al Ain 15551, Abu Dhabi, United Arab Emirates.

Abstract

We study the Sombor index and the Sombor spectral properties of chain graphs. In particular, an explicit formula for the Sombor index is given, the Sombor eigenvalues are discussed, bounds on the largest and the smallest Sombor eigenvalues are presented, chain graphs with the simple Sombor eigenvalue are characterized, formulae for the Frobenius norm and the determinant of the Sombor quotient matrix of chain graphs are given, the Sombor spread bound and the Sombor energy bounds are presented along with the characterization of graphs attaining them.

Keywords: 05C50; 15A18; Adjacency matrix; Chain graphs; Sombor eigenvalues; Sombor energy; Sombor matrix.