The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability eval...The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability evaluation of systems is important to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of graph G（V, E） is a kind of measure for the reliability of interconnection systems, which is defined as the minimum cardinality of a subset of edge set, if any, whose deletion disconnects G and such that every re- maining component has at least h vertices. This paper shows that the h-extra edge-connectivity 2n-1 2n-1 of the hypercube Qn is a constant 2n-1 for 2n-1/3≤ h2n-1, and n ≥ 4, which extends the result of [Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes, Discrete Applied Mathematics, 2013, 161（16）： 2753-2757].展开更多
基金Supported by the National Natural Science Foundation of China(11171283,11471273,11461038,11301440)Natural Sciences Foundation of Shanxi Province(2014021010-2)
文摘The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability evaluation of systems is important to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of graph G（V, E） is a kind of measure for the reliability of interconnection systems, which is defined as the minimum cardinality of a subset of edge set, if any, whose deletion disconnects G and such that every re- maining component has at least h vertices. This paper shows that the h-extra edge-connectivity 2n-1 2n-1 of the hypercube Qn is a constant 2n-1 for 2n-1/3≤ h2n-1, and n ≥ 4, which extends the result of [Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes, Discrete Applied Mathematics, 2013, 161（16）： 2753-2757].
