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It is known that every hypercube Q n is a bipartite graph. Assume that n 2 and F is a subset of edges with |F | n − 2. We prove that there exists a hamiltonian path in Q n − F between any two vertices of different partite sets. Moreover, there exists a path of length 2 n − 2 between any two vertices of the same partite set. Assume that n 3 and F is a subset… (More)

—The classical problem of diagnosability is discussed widely and the diagnosability of many well-known networks have been explored. In this paper, we consider the diagnosability of a family of networks, called the Matching Composition Network (MCN); two components are connected by a perfect matching. The diagnosability of MCN under the comparison model is… (More)

—Diagnosis is an essential subject for the reliability of a multiprocessor system. Under the comparison diagnosis model, Sengupta and Dahbura proposed a polynomial-time algorithm with time complexity OðN 5 Þ to identify all the faulty processors for a given syndrome in a system with N processors. In this paper, we present a novel idea on system diagnosis… (More)

—Diagnosability is an important factor in measuring the reliability of an interconnection network, while the (node) connectivity is used to measure the fault tolerance of an interconnection network. We observe that there is a close relationship between the connectivity and the diagnosability. According to our results, a t-regular and t-connected network… (More)

A bipartite graph is bipancyclic if it contains a cycle of every even length from 4 to |V (G)| inclusive. It has been shown that Q n is bipancyclic if and only if n 2. In this paper, we improve this result by showing that every edge of Q n − E lies on a cycle of every even length from 4 to |V (G)| inclusive where E is a subset of E(Q n) with |E | n − 2. The… (More)

The star graph possess many nice topological properties. Edge fault tolerance is an important issue for a network since the edges in the network may fail sometimes. In this paper, we show that the n-dimensional star graph is (n À 3)-edge fault tolerant hamil-tonian laceable, (n À 3)-edge fault tolerant strongly hamiltonian laceable, and (n À 4)-edge fault… (More)