On Albertson spectral properties of graphs with self-loops
DOI:
https://doi.org/10.13069/jacodesmath.v13i1.359Keywords:
Self-loops, Albertson matrix, Albertson energyAbstract
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.
Accepted: 3 August 2025
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