Some new results on the Seidel energy of graphs with self-loops

TL;DR

This paper extends the concept of Seidel energy to graphs with self-loops, providing conditions for energy equality, and explores how certain graph operations affect Seidel energy.

Contribution

It offers a necessary and sufficient condition for Seidel energy equality between a looped graph and its underlying graph, and analyzes the impact of graph operations on Seidel energy.

Findings

Seidel energy equality characterized for looped graphs

Union of graphs analyzed for Seidel energy behavior

Operations like complement and Seidel switching preserve Seidel energy

Abstract

Harshitha et al. recently introduced Seidel energy of graphs with self loops. In this paper, we extend some of their results by giving a necessary and sufficient condition for the Seidel energy of a looped graph to be equal to the Seidel energy of its underlying graph. We also consider Seidel energy of the union of certain graphs, and show that graph operations complement and Seidel switching preserve Seidel energy in the looped setting.