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The hypercube network n Q has become one of the most popular interconnection networks for its simple structure and nice properties. The crossed cube n CQ is an attractive alternative for the ordinary hypercube. It is a more generalized version of the twisted hypercube which is obtained by interchanging a pair of edges of the ordinary hypercube. Both the crossed cube and the ordinary hypercube have the same number of vertices and the same node degree. Recent research studies have revealed that the crossed cube, as an interconnection network, possesses many desirable properties which are not available in ordinary hypercube [1]. The crossed cube has a half diameter of the hypercube approximately [2]. Also it contains the optimal complete binary tree as subgraph whereas the ordinary hypercube does not[3]. In this paper, we supply the topological property of the two network structures by proving lower bounds of all-terminal reliability and node-connected reliability, and draw a conclusion that the crossed cube is superior to the hypercube in the lower bound of two kinds of reliability.

The comparison of reliability of the hypercube and crossed cube