On Graph Embedding of Crossed Cube-Connected Ring Networks

Crossed cube is a variation of hypercube, but some properties of the former are superior to those of the latter. However, it is difficult to upgrade crossed cube networks. For example, it is necessary to double the number of nodes to upgrade crossed cube networks. 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 needs to be added a crossed cube. In this paper, we prove that, if nges3, any circle of length l (4leslles2ⁿ) can be embedded into CRN(m, n) with dilation 1, and if nges3, CRN(m, n) is Hamilton-connected. It shows that CRN maintains the Hamilton-connectivity and pancyclicity of crossed cube.