Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes

Tsai, Chang-Hsiung; Lai, Yung-Chun

doi:10.1016/j.ins.2007.06.013

Cited by 56 publications

(27 citation statements)

References 14 publications

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“…Tsai [136] improved this result by showing that Q n is (2n − 5)-edge-fault-tolerant 4-bipancyclic provided n 3 and any vertex is incident with at least two fault-free edges. This is improved by Tsai and Lai [139], Shih et al [130], independently, by showing that Q n is (2n − 5)-edge-fault-tolerant edge-6-bipancyclic and any vertex is incident with at least two fault-free edges for n 3. Recently, these results have been further improved as follows.…”

Section: Theorem 22 (Tsai and Jiangmentioning

confidence: 99%

Survey on path and cycle embedding in some networks

2009

Front. Math. China

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To find a cycle (resp. path) of a given length in a graph is the cycle (resp. path) embedding problem. To find cycles of all lengths from its girth to its order in a graph is the pancyclic problem. A stronger concept than the pancylicity is the panconnectivity. A graph of order n is said to be panconnected if for any pair of different vertices x and y with distance d there exist xy-paths of every length from d to n. The pancyclicity or the panconnectivity is an important property to determine if the topology of a network is suitable for some applications where mapping cycles or paths of any length into the topology of the network is required. The pancyclicity and the panconnectivity of interconnection networks have attracted much research interest in recent years. A large amount of related work appeared in the literature, with some repetitions. The purpose of this paper is to give a survey of the results related to these topics for the hypercube and some hypercube-like networks.

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Section: Theorem 22 (Tsai and Jiangmentioning

confidence: 99%

Survey on path and cycle embedding in some networks

2009

Front. Math. China

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“…the number of its vertices is 2 n [8][9][10]13]. Some papers [2,4,5] investigated the following problem: Given a set of prescribed edges in a hypercube, which conditions guarantee the existence of a Hamiltonian cycle or path passing through all edges of this set in the hypercube?…”

Section: Introductionmentioning

confidence: 99%