Randić spectral radius and Randić energy

Let G be a simple connected graph with n vertices and let di be the degree of its i-th vertex. The Randić matrix of G is the square matrix of order n whose (i, j)-entry is equal to 1/√did j if the i-th and j-th vertex of G are adjacent, and zero otherwise. The Randić eigenvalues are the eigenvalues of the Randić matrix. The greatest Randić eigenvalue is the Randić spectral radius of G. The Randić energy is the sum of the absolute values of the Randić eigenvalues. Lower bounds for Randić spectral radius and an upper bound for Randić energy are obtained. Graphs for which these bounds are best possible are characterized.