Randić energy of specific graphs

摘要

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)−12 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.