2024/04/29 by Saeid Alikhani, Alikhani, Saeid, Nima Ghanbari +3
Computer Science · Mathematics · #05C12 #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2404.18622
openalex publication_date 2024/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.