Department of Information Management, National Chin-Yi University of Technology, Taiping, Taichung City 411, Taiwan.

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Abstract—Among the many kinds of network topologies, the crossed cube is one of the most popular. It is a variant of the hypercube with some attracting properties. A network topology is usually represented by a graph, where vertices and edges of the graph represent the nodes and communication links of the network. In this paper, we investigate the r-hyper-panconnectedness of faulty crossed cubes. A graph G is said to be r-hyper-panconnected if for any two distinct vertices x and y of G, it contains a Hamiltonian path P starting from x such that d_P (x,y)=m for any integer m satisfying r≤m≤|V(G)|-1, in which d_P (x,y) denotes the distance between x and y in P. Let 〖CQ〗_n be an n-dimensional crossed cube. We demonstrate that for any one faulty vertex w of 〖CQ〗_n and for any two distinct vertices x and y of 〖CQ〗_n-{w}, n≥5, there exists a Hamiltonian path P of 〖CQ〗_n-{w} starting from x such that d_P (x,y)=m for any integer m satisfying 2n≤m≤2^n-2. That is, the crossed cube of one vertex fault is 2n-hyper-panconnected.

Index Terms—Crossed cube, hamiltonian path, path embedding, panconnectedness.

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Cite: Hon-Chan Chen, "The R-Hyper-Panconnectedness of Faulty Crossed Cubes," Journal of Computers vol. 14, no. 1, pp. 44-51, 2019.