Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 10 2 2025 06 01 Elliptic Sombor energy of a graph 143 155 2184 10.22061/jdma.2024.11190.1089 EN Saeid Alikhani Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, I. R. Iran Nima Ghanbari Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, I. R. Iran Mohammad Ali Dehghanizadeh Department of Mathematics, National University of Skills (NUS), Tehran, I. R. Iran Journal Article 2024 08 19 Let G be a simple graph with vertex set V(G) = {v1, 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.

https://jdma.sru.ac.ir/article_2184_f41b051e4b06f4f8d1dc6dd856f02876.pdf