Energy and Randić energy of special graphs

Abstract

In this paper, we determine the Randić 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, Randicc equienergetic graphs and also, infinite families of integral graphs.