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An dimensional crossed cube, CQ,,, is a variation of hypercubes. in this paper, we give a new shortest path routing algorithm based on a new distance measure defined hsreln. In comparison with Efe's algorithm, which generates one shortest path in O(ri2) time, our algorithm can generate more shortest paths in O (n) time. Based on a given shortest path(More)
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)
In Part I of this paper we have introduced the concept of a hyperbolic exterior differential system of class s. For s = 0 these are essentially a geometric formulation of a first order quasi-linear hyperbolic PDE system in two independent and two dependent variables, with the group of contact transformations providing the allowable changes of variables. We(More)
A k-container C(u, v) of a graph G is a set of k disjoint paths joining u to v. A k-container C(u, v) is a k *-container if every vertex of G is incident with a path in C(u, v). A bipartite graph G is k *-laceable if there exists a k *-container between any two vertices u, v from different partite set of G. A bipartite graph G with connectivity k is super(More)
In this paper, we investigate the fault-tolerant capabilities of the k-ary n-cubes for even integer k with respect to the hamiltonian and hamiltonian-connected properties. The k-ary n-cube is a bipartite graph if and only if k is an even integer. Let F be a faulty set with nodes and/or links, and let k 3 be an odd integer. When |F | 2n − 2, we show that(More)