Some New Results on Seidel Equienergetic Graphs

TL;DR

This paper investigates Seidel energy in graphs, presenting new results on families of graphs that share the same Seidel energy, expanding understanding of graph eigenvalue properties.

Contribution

It introduces new families of graphs that are Seidel equienergetic, contributing to spectral graph theory by identifying specific graph classes with equal Seidel energy.

Findings

Identified graph families with equal Seidel energy

Extended the concept of graph energy to Seidel matrices

Provided theoretical results on Seidel equienergetic graphs

Abstract

The energy of a graph $G$ is the sum of the absolute values of the eigenvalues of the adjacency matrix of $G$. Some variants of energy can also be found in the literature which are defined on the concepts of Laplacian matrix, Distance matrix, Common neighbourhood matrix and Seidel matrix. The Seidel matrix of the graph $G$ is the square matrix in which $ij^{th}$ entry is $-1$ or $1$, if the vertices $v_i$ and $v_j$ are adjacent or non-adjacent respectively, and is $0$ , if $v_i=v_j.$ The Seidel energy of $G$ is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some graph families which are Seidel equienergetic.