Elliptic Sombor energy of a graph

Let G be a simple graph with vertex set V(G) = \{v_۱, v_۲,\ldots, v_n\}. The elliptic Sombor matrix of G, denoted by A_{ESO}(G), is defined as the n\times n matrix whose (i,j)-entry is (d_i+d_j)\sqrt{d_i^۲+d_j^۲} if v_i and v_j are adjacent and ۰ for another cases.Let the eigenvalues of the elliptic Sombor matrix A_{ESO}(G) be \rho_۱\geq \rho_۲\geq \ldots\geq \rho_n which are the roots of the elliptic Sombor characteristic polynomial \prod_{i=۱}^n (\rho-\rho_i). The elliptic Sombor energy {E_{ESO}} of G is the sum of absolute values of the eigenvalues of A_{ESO}(G). In this paper, we compute the elliptic Sombor characteristic polynomial and the elliptic Sombor energy for some graph classes. We compute the elliptic Sombor energy of cubic graphs of order ۱۰ and as a consequence, we see that two k-regular graphs of the same order may have different elliptic Sombor energy.

کلیدواژه ها:

Elliptic Sombor Matrix ، Elliptic Sombor Energy ، Elliptic Sombor Characteristic Polynomial ، Eigenvalues ، Regular Graphs