Panpositionable hamiltonicity and panconnectivity of the arrangement graphs

Teng, Yuan-Hsiang; Tan, Jinglu; Hsu, Lih‐Hsing

doi:10.1016/j.amc.2007.08.073

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Introduction2

Arrangement Graphs2

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Cited by 18 publications

(9 citation statements)

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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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“…For panpositionable hamiltonicity of A n,k , Teng et al [135] obtained the following result. Theorem 14.3 (Teng et al [135]) A n,k is panpositionable hamiltonian and panconnected for k 1 and n − k 2.…”

Section: Arrangement Graphsmentioning

confidence: 92%

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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“…The arrangement graph A n;k is pancyclic for n À k P 2. h Theorem 2 (Teng et al [18]). The arrangement graph A n;k is panconnected for n À k P 2. h Theorem 3 (Hsu et al [12]).…”

Section: Some Properties Of the Arrangement Graphsmentioning

confidence: 95%

“…For n À k P 2, Day and Tripathi [6] proved that A n;k is pancyclic. Teng et al [18] proved that A n;k is panconnected. Concerning fault tolerance, Hsieh et al [10] studied the existence of Hamiltonian cycles in faulty arrangement graphs.…”

Section: Introductionmentioning

confidence: 98%