L-Borderenergetic graphs and Normalized Laplacian Energy

TL;DR

This paper introduces new classes of graphs called L-borderenergetic graphs that share Laplacian energy with complete graphs and explores graphs with identical normalized Laplacian energy despite being noncospectral.

Contribution

The paper defines and constructs new L-borderenergetic graphs and identifies graphs with equal normalized Laplacian energy but different spectra, expanding spectral graph theory.

Findings

L-borderenergetic graphs are noncospectral with complete graphs but share Laplacian energy.

Identified graphs with identical normalized Laplacian energy but different spectra.

Provides new examples and properties of energy-equivalent graphs.

Abstract

In this paper we present new L-borderenergetic graphs, this is, graphs which are L-noncospectral with Kn but have the same Laplacian energy. We also present some graphs which are noncospectral to respective normalized Laplacian energy and they have the same normalized Laplacian energy.