Randic energy and Randic estrada index of a graph

Abstract

Let G be a simple connected graph with n vertices and let di be the degree of its i-th vertex. The Randi´c matrix of G is the square matrix of order n whose (i,j)-entry is equal to 1/ $sqrt{d_id_j}$ if the i-th and j-th vertex of G are adjacent, and zero otherwise. The Randi´c eigenvalues are the eigenvalues of the Randi´c matrix. The Randi´c energy is the sum of the absolute values of the Randi´c eigenvalues. In this paper, we introduce a new index of the graph G which is called Randi´c Estrada index. In addition, we obtain lower and upper bounds for the Randi´c energy and the Randi´c Estrada index of G. 2000 Mathematics Subject Classifications: 05C50,15A18