Summary: ``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] [MR3052180], 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] [MR3990661].''