In this paper, we study a new graph invariant named Resistance-Harary index, defined as RH(G) = Sigma({u,v}subset of v(G)) 1/r(G)(u,v) where r(G)(u, v) is the resistance distance between vertices u and v of a connected graph G. We establish that S-n(3) and P-n(3). are the graphs with the maximal and minimal Resistance-Harary index among all unicy...