  In this paper, we determine the Randic' energy of the m-splitting graph, the
m-shadow graph and the m-duplicate graph of a given graph, m being an arbitrary
integer. Our results allow the construction of an infinite sequence of graphs
having the same Randic' energy. Further, we determine some graph invariants
like the degree Kirchhoff index, the Kemeny's constant and the number of
spanning trees of some special graphs. From our results, we indicate how to
obtain infinitely many pairs of equienergetic graphs, Randic' equienergetic
graphs and also, infinite families of integral graphs.
