Let G be a graph of order n, and diβ the degree of a vertex viβ of
G. The Randi\'c matrix R=(rijβ) of G is defined by rijβ=1/djβdjββ if the vertices viβ and vjβ are adjacent in G and
rijβ=0 otherwise. The normalized signless Laplacian matrix Q is
defined as Q=I+R, where I is the identity matrix. The
Randi\'c energy is the sum of absolute values of the eigenvalues of R.
In this paper, we find a relation between the normalized signless Laplacian
eigenvalues of G and the Randi\'c energy of its subdivided graph S(G). We
also give a necessary and sufficient condition for a graph to have exactly k
and distinct Randi\'c eigenvalues.Comment: 7 page