Randi Ìc Energy and Randi Ìc Estrada Index of a Graph

Abstract

Let G be a simple connected graph with n vertices and let d be the degree of its i-th vertex. The Randi Ìc matrix of G is the square matrix of order n whose i, j -entry is equal to 1/ di dj if the i-th and j-th vertex of G are adjacent, and zero otherwise. The Randi Ìc eigenvalues are the eigenvalues of the Randi Ìc matrix. The Randi Ìc energy is the sum of the absolute values of the Randi Ìc eigenvalues. In this paper, we introduce a new index of the graph G which is called Randi Ìc Estrada index. In addition, we obtain lower and upper bounds for the Randi Ìc energy and the Randi Ìc Estrada index of G.