2014/11/10 by Saeid Alikhani, Alikhani, Saeid, Nima Ghanbari +1
Chemistry · Mathematics · #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.1411.2544
openalex publication_date 2014/11/10 · 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 Randić matrix of G, denoted by R(G), is defined as the n× n matrix whose (i,j)-entry is (didj)(-1)/(2) if vi and vj are adjacent and 0 for another cases. Let the eigenvalues of the Randić matrix R(G) be ρ1≥ ρ2≥ ...≥ ρn which are the roots of the Randić characteristic polynomial ∏i=1n (ρ-ρi). The Randić energy RE of G is the sum of absolute values of the eigenvalues of R(G). In this paper we compute the Randić characteristic polynomial and the Randić energy for specific graphs G.