Cognitive radio is an emerging technique to improve the utilization of radio frequency spectrum in wireless communication networks. That is, spectrum efficiency can be increased significantly by giving opportunistic access of the frequency bands to a group of cognitive users to whom the band has not been licensed. In this paper, as a cross layer application (MAC and physical layers) of graph theory, we consider the problem of throughput maximization of spectrum allocation in cognitive radio networks under interference constraint. We propose a novel auction-based channel allocation mechanism which tries to maximize both total and primary users' utilities while satisfying signal to interference ratio constraint on primary receivers so that transmitted packets will be successfully received, without controlling secondary user powers. For comparison we discuss a greedy algorithm as well, however, one that does not handle interference issue. In order to compare results of proposed and greedy algorithms, we propose net throughput by taking into account outage probability of primary receiver. Simulation results show that exposing higher SINR (outage) threshold not only decreases total gain and primary users' utilities but also worsens channel distribution performance. On the other hand adding auction mechanism significantly increases total gain throughput and primary user' s utility. Particularly, up to SINR threshold values of 20 dBs, auction provides outstanding performance and proposed algorithm has total throughput results close to those of the greedy one even though no interference constraint is applied in the greedy algorithm. Another noticeable point of simulation results is crossover of net throughputs of proposed and greedy algorithms at a SINR threshold level after which results of ABSA-UNIC and NASA-UNIC are much better. This clearly shows superiority of proposed mechanism.