Elliptic Sombor energy of a graph

Let G be a simple graph with vertex set V (G) = \v₁, v₂, , vₙ\. The elliptic Sombor matrix of G, denoted by A₄ₒ₎ (G), is defined as the n n matrix whose (i, j) -entry is (dᵢ+dⱼ) dᵢ²+dⱼ² if vᵢ and vⱼ are adjacent and 0 for another cases. Let the eigenvalues of the elliptic Sombor matrix A₄ₒ₎ (G) be ₁ ₂ ₙ which are the roots of the elliptic Sombor characteristic polynomial ₈=₁ⁿ (-ᵢ). The elliptic Sombor energy E₄ₒ₎ of G is the sum of absolute values of the eigenvalues of A₄ₒ₎ (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 10 and as a consequence, we see that two k-regular graphs of the same order may have different elliptic Sombor energy.