Eccentricity Laplacian energy of a graph
Document Type
Article
Publication Title
Nanosystems: Physics, Chemistry, Mathematics
Abstract
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 elij, where elij is −1 if the corresponding vertices are adjacent, elii is the eccentricity of vi for 1 ≤ i ≤ n, and elij is 0 otherwise. If ɛ1, ɛ2, …, ɛn are the eigenvalues of the n∑ eccentricity Laplacian matrix, then the eccentricity Laplacian energy of G is ELE(G) = |ɛi − 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 π−electron energy is obtained. i=1.
First Page
567
Last Page
575
DOI
10.17586/2220-8054-2024-15-5-567-575
Publication Date
10-1-2024
Recommended Citation
Harshitha, A.; Nayak, S.; and D’Souza, S., "Eccentricity Laplacian energy of a graph" (2024). Open Access archive. 9947.
https://impressions.manipal.edu/open-access-archive/9947
