On the double-vertex-cycle-connectivity of crossed cubes
Xiaofan Yang, Graham M. Megson · International Journal of Parallel Emergent and Distributed Systems · 2004
Crossed cube, a variation of hypercube, is a candidate for the interconnection network topology employed in parallel computing systems due to nearly half diameter and stronger subgraph embedding capabilities. Existence of various cycles (rings) in an interconnection network is essential for parallel algorithms that communicate data in token-ring mode. This paper addresses the existence of cycles with some specified properties in an n-dimensional crossed cube, CQ n . We first propose the notion of double-vertex-cycle-connectivity for a graph, which provides a new measure of cycle embedding capability of the graph. We then prove that, for any two distinct vertices on CQ n at a distance of d apart and each integer l satisfying 2d + 6 \leq l \leq \vert V(CQ_{n}) \vert , CQ n contains a cycle of length l that goes through the two vertices. Due to the fact that a hypercube does not share these properties, crossed cube shows stronger cycle embedding capability than hypercube.