Eccentricity Laplacian energy of a graph

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 ≤ i ≤ n, and el_ij is 0 otherwise. If ɛ₁, ɛ₂, …, ɛ_n are the eigenvalues of the n∑ eccentricity Laplacian matrix, then the eccentricity Laplacian energy of G is ELE(G) = |ɛ_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 π−electron energy is obtained. i=1.