2021/08/19 by Nima Ghanbari, Ghanbari, Nima · 2 citations
Mathematics · Chemistry · Computer Science · #Graph theory and applications #Molecular spectroscopy and chirality #Computational Drug Discovery Methods
paper · pdf · doi:10.48550/arxiv.2108.08552
Let G be a simple graph with vertex set V(G) = \v1, v2,…, vn\. The Sombor matrix of G, denoted by ASO(G), is defined as the n× n matrix whose (i,j)-entry is √(di2+dj2) if vi and vj are adjacent and 0 for another cases. Let the eigenvalues of the Sombor matrix ASO(G) be ρ1≥ ρ2≥ …≥ ρn which are the roots of the Sombor characteristic polynomial ∏i=1n (ρ-ρi). The Sombor energy EnSO of G is the sum of absolute values of the eigenvalues of ASO(G). In this paper we compute the Sombor characteristic polynomial and the Sombor energy for some graph classes, define Sombor energy unique and propose a conjecture on Sombor Energy.