In this paper, we present an optimal scheme for power allocation and relay selection in a cognitive radio network where a pair of cognitive (or secondary) transceiver nodes communicate with each other assisted by a set of cognitive two-way relays. The secondary nodes share the spectrum with a licensed primary user (PU), and each node is assumed to be equipped with a single transmit/receive antenna. The interference to the PU resulting from the transmission from the cognitive nodes is kept below a specified limit. We propose joint relay selection and optimal power allocation among the secondary user (SU) nodes achieving maximum throughput under transmit power and PU interference constraints. A closed-form solution for optimal allocation of transmit power among the SU transceivers and the SU relay is presented. Furthermore, numerical simulations and comparisons are presented to illustrate the performance of the proposed scheme.