Cognitive Wireless Mesh Network (CWMN) is an opportunistic network in which radio channels can be assigned according to their availability to establish connections among nodes. After establishing a radio connection among nodes, it is necessary to find an optimal route from the source node to the destination node in the network. If there remain more channels among nodes, the minimum weighted channel should be taken into account to establish expected routes. The graph theoretic approach fails to model the multi-channel cognitive radio networks due to abrupt failure in finding new successful routes as it can’t figure multi-channel networks. In this paper, a multi-edged graph model is being proposed to overcome the problems of cognitive radio networks, such as flooding problems, channel accessing problems etc. A new channel accessing algorithm has been introduced, and optimal routes have been selected using a heuristic algorithm named RBFS. Simulation results are compared with DJKSTRA based routing protocols.