# On eccentricity version of Laplacian energy of a graph

## TL;DR

This paper introduces and investigates an eccentricity-based variant of Laplacian energy in graphs, extending existing spectral graph theory concepts with a focus on eccentricity measures.

## Contribution

It proposes a new eccentricity-based Laplacian energy measure and explores its properties, expanding the spectral graph theory framework.

## Key findings

- Defined the eccentricity Laplacian energy of a graph.
- Derived properties and bounds for the new energy measure.
- Compared the eccentricity Laplacian energy with existing graph energies.

## Abstract

The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and average degree of the vertices of G. Motivated by the work from Sharafdini et al. [R. Sharafdini, H. Panahbar, Vertex weighted Laplacian graph energy and other topological indices. J. Math. Nanosci. 2016, 6, 49-57.], in this paper we investigate the eccentricity version of Laplacian energy of a graph G.