关键词: Hamilton连通性, pancyclicity性, 交叉立方体环, 交叉立方体, 超立方体

Abstract: Crossed cube is a variation of hypercube, but some properties of the former are superior to those of the latter. For example, the diameter of crossed cube is approximately half that of the hyper cube; if n≥3, the crossed cube CQn is Hamilton-connected; if n≥2, any circle of length l(4≤ l ≤2n )can be embedded into the crossed cube CQn with dilation 1, that is pancyclicity of crossed cube. However, it is necessary to double the number of nodes to upgrade crossed cube like hypercube. As a kind of hierarchical ring interconnection networks HRN, crossed cube-connected ring interconnection network CRN can effectively overcome the disadvantage. When upgraded, it only need to be added a crossed cube. In this paper, we prove that CRN still maintains the Hamilton –connectivity and pancyclicity of crossed cube.

Key words: Hamilton-connectivity, pancyclicity, crossed cube-connected ring, crossed cube, hypercube