m-ary n-cube (denoted by Q_n(m)) is an important network topology for parallel processing computer systems. Some methods of forming big cycle from small cycles and links have been developed. Basing on which, we has proved that in m-ary n-cube, there exists a cycle of every length from 3 to |V(G)| inclusive and all kinds of length cycles have been constructed in. This important Hamilton property of m-ary n-cube can be applied in the topology design of computer networks to improve the network performance.

In this paper a new algorithm for fault-tolerant routing based on depth-first search Is developed. Its performance is analyzed for m-ary n-cube networks in presence of an arbitrary number of components being damaged. We derive an exact expression for the probability of routing messages via optimal paths from the source node to obstructed node. The probability of routing messages via an optimal path between any two nodes is a special case of our results, and can be obtained by replacing the obstructed node with the destination node. It is also showed that in the presence of component failures the new algorithm can route messages via an optimal path to its destination with a very high probability.