More on energy and Randi´c energy of specific graphs

Abstract

Let G be a simple graph of order n. The energy E(G) of the graph G is the sum of the absolute
values of the eigenvalues of G. The Randi´c 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. The
Randi´c energy RE of G is the sum of absolute values of the eigenvalues of R(G). In this paper
we compute the energy and Randi´c energy for certain graphs. Also we propose a conjecture on
Randi´c energy.