The radio resource allocation in wireless communication is analysed in this paper. Pair of users communicates each other through multiple two way relays in orthogonal frequency division multiplexing transmission systems. The total throughput is maximized by relay selection, channel and relay assignment, subcarrier pairing and subcarrier allocation by prim’s algorithm. The graphical theory approach has used to solve the problem optimally in polynomial time. The evaluation of the network total throughput with respect to transmit power node and the number of relay nodes are analysed through simulation. In this work, the improvement in sum rate with optimum carrier assignment using proposed algorithm is demonstrated against the classical work. © School of Engineering, Taylor’s University.