交叉立方体环的Hamilton连通性和Pancyclicity性

交叉立方体是超立方体互连网络的一种变型,它的某些性质优于超立方体。例如,其直径几乎是超立方体的一半;当n≥3,交叉立方体CQn具有Hamilton连通性;当n≥2,所有长度在4到2n之间的圈都能够以扩张1嵌入CQn,即交叉立方体具有Pancyclity性。但是,交叉立方体同超立方体一样,当需要升级时,必须成倍增加结点。交叉立方体环互连网络CRN作为层次环互连网络HRN8]的一种,可以有效地克服这个缺点,当需要升级时,只需在环上增加一个交叉立方体。在文中,证明了交叉立方体环互连网络仍然保持了交叉立方体具有的Hamilton连通性和Pancyclity性。

Hamilton-connectivity and Pancyclicity of Crossed Cube-connected Ring

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.