Embedding of cycles in arrangement graphs

Day, Khaled; Tripathi, Anand

doi:10.1109/12.238494

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2012

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Cited by 71 publications

(21 citation statements)

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“…The cycle embedding problem is investigated in a lot of interconnection networks [4,5,9,10,12,15]. In general, a graph is of pancyclicity if it contains cycles of all length [2].…”

Section: Introductionmentioning

confidence: 99%

Edge-fault-tolerant edge-bipancyclicity of hypercubes

2005

Information Processing Letters

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“…The cycle embedding problem is investigated in a lot of interconnection networks [4,5,9,10,12,15]. In general, a graph is of pancyclicity if it contains cycles of all length [2].…”

Section: Introductionmentioning

confidence: 99%

Edge-fault-tolerant edge-bipancyclicity of hypercubes

2005

Information Processing Letters

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“…On the other hand, it was shown in [10] that when n − k ≥ 2 the arrangement graph is pancyclic, that is, contains cycles of all possible lengths. In [14], a longest fault-free cycle was established in an arrangement graph with faulty edges and/or faulty vertices.…”

Section: Introductionmentioning

confidence: 96%

Embedding longest fault-free paths in arrangement graphs with faulty vertices

Chen

2001

Networks

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The arrangement graph is a generalization of the star graph. Recent work by Hsieh et al. showed that an arrangement graph with faulty vertices contains a longest fault‐free cycle. In this paper, we generalize Hsieh et al.'s result by constructing a longest fault‐free path between two arbitrary distinct healthy vertices. Moreover, our result can tolerate more faulty vertices than can Hsieh et al.'s result. The situation of simultaneous faulty vertices and faulty edges is also discussed. © 2001 John Wiley & Sons, Inc.

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“…A result given in [17] showed that the r-dimensional star graph contains all cycles of even length k where 6 Յ k Յ r!. Furthermore, a common generalization of star graphs and alternating group graphs, called arrangement graphs, has been proven to be pancyclic provided that the graph is not a star graph [9].…”

Section: Introductionmentioning

confidence: 98%