A new shortest path routing algorithm and embedding cycles of crossed cube

An n-dimensional crossed cube, CQ_n, is a variation of hypercubes. In this paper, we give a new shortest path routing algorithm based on a new distance measure defined herein. In comparison with Efe´s algorithm which generates one shortest path in O(n²) time, our algorithm can generate more shortest paths in O(n) time. Furthermore, we show that CQ_n is a pancyclic network and we construct various types of cycles of an arbitrary length at least four