Abstract:
The Randić energy RE(G) of a graph G is defined as the sum of the absolute
values of the eigenvalues of its Randić matrix. In [8], Rojo et.al. has obtained the
construction of bipartite graph having the same Randić energy by using a new graph
operation. In this paper we define a graph operation for any graph and construct the
graphs with the same Randić energy. Also, we obtain bipartite graphs which have
the same Randić energy with path graphs from a new concept (mixed extension of
graphs) introduced by Haemers in [6].