Path bipancyclicity of hypercubes

Tsai, Chang-Hsiung; Jiang, Shuyun

doi:10.1016/j.ipl.2006.08.011

Cited by 20 publications

(21 citation statements)

References 6 publications

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“…Parallel algorithms for solving algebraic and graph problems are based on a path architecture [1,20]. The path embedding problem has attracted intensive studies in various networks in the literature [11][12][13][14]18,[23][24][25][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Two node-disjoint paths in balanced hypercubes

Cheng

Hao

Feng

2014

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Two node-disjoint paths in balanced hypercubes

Cheng

Hao

Feng

2014

Applied Mathematics and Computation

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“…Li et al [110] improved this result by proving that Q n is edge-bipancyclic for n 2. Recently, Tsai and Jiang [138] proposed a stronger concept than edgebipancyclicity, called the path bipancyclicity. A bipartite graph G of order n is k-path bipancyclic if every path P of length m lies in a cycle of every even length from max{4, 2m} to n inclusive, where 1 m k. From this definition, it is clear that every k-path bipancyclic graph is edge-bipancyclic where k 1.…”

Section: Hypercubesmentioning

confidence: 99%

“…A bipartite graph G of order n is k-path bipancyclic if every path P of length m lies in a cycle of every even length from max{4, 2m} to n inclusive, where 1 m k. From this definition, it is clear that every k-path bipancyclic graph is edge-bipancyclic where k 1. [138]) Q n is (2n − 4)-path bipancyclic for n 3.…”

Section: Hypercubesmentioning

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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“…Sun et al proved that the ndimensional hypercube Q n contains n mutually independent Hamiltonian cycles for n ≥ 4 [28]. Other studies about hypercubes are in [4,5,9,12,21,25,[29][30][31]33].…”

Section: Preliminariesmentioning

confidence: 99%

Mutually independent Hamiltonian cycles in dual-cubes

et al. 2009

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The hypercube family Q n is one of the most well-known interconnection networks in parallel computers. With Q n , dual-cube networks, denoted by DC n , was introduced and shown to be a (n + 1)-regular, vertex symmetric graph with some fault-tolerant Hamiltonian properties. In addition, DC n 's are shown to be superior to Q n 's in many aspects. In this article, we will prove that the n-dimensional dual-cube DC n contains n + 1 mutually independent Hamiltonian cycles for n ≥ 2. More specifically, let v i ∈ V (DC n ) for 0 ≤ i ≤ |V (DC n )| − 1 and let v 0 , v 1 , . . . , v |V (DC n )|−1 , v 0 be a Hamiltonian cycle of DC n . We prove that DC n contains n +1 Hamiltonian cycles of the form v 0 , v k 1 , . . . , v k |V (DC n )|−1 , v 0 for 0 ≤ k ≤ n, in which v k i = v k i whenever k = k . The result is optimal since each vertex of DC n has only n + 1 neighbors.

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Path bipancyclicity of hypercubes

Cited by 20 publications

References 6 publications

Two node-disjoint paths in balanced hypercubes

Two node-disjoint paths in balanced hypercubes

Survey on path and cycle embedding in some networks

Mutually independent Hamiltonian cycles in dual-cubes

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