Sombor spectra of chain graphs

Muhammad Imran; Bilal Ahmad Rather

doi:10.1016/j.heliyon.2023.e18135

Sombor spectra of chain graphs

Muhammad Imran, Bilal Ahmad Rather

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Article number	e18135
Journal	Heliyon
Volume	9
Issue number	7
DOIs	https://doi.org/10.1016/j.heliyon.2023.e18135
Publication status	Published - Jul 2023

Keywords

Adjacency matrix
Chain graphs
Sombor eigenvalues
Sombor energy
Sombor matrix

ASJC Scopus subject areas

General

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10.1016/j.heliyon.2023.e18135

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AB - 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.

KW - Adjacency matrix

KW - Chain graphs

KW - Sombor eigenvalues

KW - Sombor energy

KW - Sombor matrix

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Sombor spectra of chain graphs

Abstract

Keywords

ASJC Scopus subject areas

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