On Albertson spectral properties of graphs with self-loops

K. V. Madhumitha; Sabitha D’Souza; Swati Nayak

doi:10.13069/jacodesmath.v13i1.359

On Albertson spectral properties of graphs with self-loops

K. V. Madhumitha
, Sabitha D’Souza
, Swati Nayak^*

^*Corresponding author for this work

School of Basic Sciences, Humanities and Management

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

Abstract

The Albertson irregularity measure is defined as Alb(Γ) = Σ_uvεE(Γ) |d(u) - d(v)|. In this work, the concept of Albertson energy is extended from simple graphs to graphs with self-loops. Also the expression for the Albertson eigenvalues of a graph with self-loops are given. Some bounds on the Albertson energy of graphs with self-loops and the spread of Alb(Γ_S) are obtained. In the last section, the Albertson energy of complete, complete bipartite, crown and thorn graphs with self-loops are computed.

Original language	English
Pages (from-to)	75-89
Number of pages	15
Journal	Journal of Algebra Combinatorics Discrete Structures and Applications
Volume	13
Issue number	1
DOIs	https://doi.org/10.13069/jacodesmath.v13i1.359
Publication status	Published - 22-12-2025

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.13069/jacodesmath.v13i1.359

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abstract = "The Albertson irregularity measure is defined as Alb(Γ) = ΣuvεE(Γ) |d(u) - d(v)|. In this work, the concept of Albertson energy is extended from simple graphs to graphs with self-loops. Also the expression for the Albertson eigenvalues of a graph with self-loops are given. Some bounds on the Albertson energy of graphs with self-loops and the spread of Alb(ΓS) are obtained. In the last section, the Albertson energy of complete, complete bipartite, crown and thorn graphs with self-loops are computed.",

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AU - D’Souza, Sabitha

AU - Nayak, Swati

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N2 - The Albertson irregularity measure is defined as Alb(Γ) = ΣuvεE(Γ) |d(u) - d(v)|. In this work, the concept of Albertson energy is extended from simple graphs to graphs with self-loops. Also the expression for the Albertson eigenvalues of a graph with self-loops are given. Some bounds on the Albertson energy of graphs with self-loops and the spread of Alb(ΓS) are obtained. In the last section, the Albertson energy of complete, complete bipartite, crown and thorn graphs with self-loops are computed.

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On Albertson spectral properties of graphs with self-loops

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