The radio channel assignment problem can be cast as a graph coloring problem. Vertices correspond to transmitter locations and their labels (colors) to radio channels. The assignment of frequencies to each transmitter (vertex) must avoid interference which depends on the seperation each pair of vertices has. Two levels of interference are assumed in the problem we are concerned. Based on this channel assignment problem, we proposed a graph labelling problem which has two constraints instead of one. We consider the question of finding the minimum edge of this labelling. Several classes of graphs including one that is important to a telecommunication problem have been studied.