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—Previous works on edge-fault tolerance with respect to hypercubes Q n are mainly focused on 1-edge fault and 2-or 3-edge fault with limited size of n. We give a construction scheme for 2-EFT(Q n) graphs and 3-EFT(Q n) graphs, where n is arbitrarily large. In our constructions, approximately log n extra degree is added to the vertices of Q n for… (More)

Fault-tolerant multiprocessors are widely used in on-line transaction processing. Fault tolerance is also desirable in massively parallel systems that have a relatively high failure probability. Two types of failures in a multiprocessor system are of interest, processor failures and link failures. Most of the previous research in designing optimal… (More)

A k-container C(u, v) of G between u and v is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k *-container if it contains all nodes of G. A graph G is k *-connected if there exists a k *-container between any two distinct nodes. The spanning connectivity of G, κ * (G), is defined to be the largest integer k such that G… (More)

Let P 1 = =v u n be two hamiltonian paths of G. We say that P 1 and P 2 are independent if u 1 = v 1 , u n = v n , and u i = v i for 1 < i < n. We say a set of hamiltonian paths P 1 , P 2 ,. .. , P s of G between two distinct vertices are mutually independent if any two distinct paths in the set are independent. We use n to denote the number of vertices and… (More)

Assume that n and δ are positive integers with 2 ≤ δ < n. Let h(n, δ) be the minimum number of edges required to guarantee an n-vertex graph with minimum degree δ(G) ≥ δ to be hamiltonian, i.e., any n-vertex graph G with δ(G) ≥ δ is hamiltonian if |E(G)| ≥ h(n, δ). We prove that h(n, δ) = C(n − δ, 2) + δ 2 + 1 if 1 3 ((1) mod 2) , 6 n n δ + + × + ≤ ⎢ ⎥ ⎣ ⎦… (More)

Ž. X Given a series-parallel network network, for short N, its dual network N is given by interchanging the series connection and the parallel connection of network N. We usually use a series-parallel graph to represent a network. Let w x w X x 1 2 k w x w X x w x trail on both G N and G N. If a common trail covers all of the edges in G N w X x and G N , it… (More)

A graph G is said to be Hamiltonian-connected if there is a Hamiltonian path between every two distinct nodes of G. Let F denote the set of faulty nodes of G. Then, G is |F |-node Hamiltonian-connected if G − F is Hamiltonian-connected. We use K(d, t) to denote a WK-recursive network of level t, each of whose basic modules is a d-node complete graph.… (More)