Eccentricity Laplacian energy of a graph

A. Harshitha ; S. Nayak ; S. D'Souza

Nanosistemy: fizika, himiâ, matematika, Tome 15 (2024) no. 5, pp. 567-575.

Résumé

Let $G$ be a simple, finite, undirected and connected graph. The eccentricity of a vertex $v$ is the maximum distance from $v$ to all other vertices of $G$. The eccentricity Laplacian matrix of $G$ with $n$ vertices is a square matrix of order $n$, whose elements are $el_{ij}$, where $el_{ij}$ is $-1$ if the corresponding vertices are adjacent, $el_{ii}$ is the eccentricity of $v_i$ for $1\le i\le n$, and $el_{ij}$ is $0$ otherwise. If $\epsilon_1, \epsilon_1, \dots,\epsilon_n$ are the eigenvalues of the eccentricity Laplacian matrix, then the eccentricity Laplacian energy of $G$ is $ELE(G)=\sum_{i=1}^n|\epsilon_i-avec(G)|$, where $avec(G)$ is the average eccentricities of all the vertices of $G$. In this study, some properties of the eccentricity Laplacian energy are obtained and comparison between thge eccentricity Laplacian energy and the total $\pi$-electron energy is obtained.

Détail

Keywords: eccentricity, Laplacian energy.
Mots-clés : distance