Elliptic Sombor energy of a graph

Let G be a simple graph with vertex set V(G) = ₁, v₂,…, vₙ\. The elliptic Sombor matrix of G, denoted by AESO(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 AESO(G) be ρ₁≥ ρ₂≥ …≥ ρₙ which are the roots of the elliptic Sombor characteristic polynomial ∏ᵢ₌₁ⁿ (ρ-ρᵢ). The elliptic Sombor energy EESO of G is the sum of absolute values of the eigenvalues of AESO(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.