On Albertson spectral properties of graphs with self-loops

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

doi:10.13069/jacodesmath.v13i1.359

K. V. Madhumitha Department of Mathematics, Manipal Institute of Technology
Sabitha D'Souza Department of Mathematics, Manipal Institute of Technology
Swati Nayak Department of Mathematics, Manipal Institute of Technology

DOI: https://doi.org/10.13069/jacodesmath.v13i1.359

Keywords: Self-loops, Albertson matrix, Albertson energy

Abstract

The Albertson irregularity measure is defined as $Alb(\Gamma)=\sum_{uv\in E(\Gamma)} \vert d(u)-d(v)\vert.$ 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 $Alb(\Gamma_S)$ are obtained. In the last section, the Albertson energy of complete, complete bipartite, crown and thorn graphs with self-loops are computed.