Pancyclicity and bipancyclicity of folded hypercubes with both vertex and edge faults

Kuo, Che-Nan

doi:10.1016/j.tcs.2015.08.018

Cited by 11 publications

(3 citation statements)

References 23 publications

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“…The n-dimensional enhanced hypercube Q n,k (1 ≤ k ≤ n − 1) is proposed to improve the efficiency of the hypercube structure Q n , as it possesses many attractive properties that are superior to that of the hypercube [4][5][6][7][8][9][10][11]. Moreover, the folded hypercube FQ n is the special case of the enhanced hypercube Q n,k when k = 1 [12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Cycle Embedding in Enhanced Hypercubes with Faulty Vertices

Liu

2023

Symmetry

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The enhanced hypercube is a well-known variant of the hypercube and can be constructed from a hypercube by adding an edge to every pair of vertices with complementary addresses. Let Fv denote the set of faulty vertices in an n-dimensional enhanced hypercube Qn,k(1≤k≤n−1). In this paper, we conclude that if n≥2, then every fault-free edge of Qn,k−Fv lies on a fault-free cycle of every even length from 4 to 2n−2|Fv|, and if n(≥2) and k have the different parity, then every fault-free edge of Qn,k−Fv lies on a fault-free cycle of every possible odd length from n−k+4 to 2n−2|Fv|−1, where |Fv|≤n−2.

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Section: Introductionmentioning

confidence: 99%

“…Problems regarding the fault-tolerant embedding for hypercubes and folded hypercubes have been studied in [14,15,23,24]. Let F v and F e be the sets of faulty vertices and faulty edges, respectively.…”

Section: Introductionmentioning

confidence: 99%

Cycle Embedding in Enhanced Hypercubes with Faulty Vertices

Liu

2023

Symmetry

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“…Hence, the issue of fault-tolerant cycle embedding in an n-dimensional folded hypercube F Q n has been studied in [2,5,7,8,9,10,11,12,13,14,20,19]. Embedding cycles in networks is important as many network algorithms utilize cycles as data structure.…”

Section: Introductionmentioning

confidence: 99%

Edge-pancyclicity and edge-bipancyclicity of faulty folded hypercubes

Kuo

Stewart

2016

Theoretical Computer Science

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Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractLet F v and F e be sets of faulty vertices and faulty edges, respectively, in the folded hypercube F Q n so that |F v | + |F e | ≤ n − 2, for n ≥ 2. Choose any fault-free edge e. If n ≥ 3 then there is a fault-free cycle of length l in F Q n containing e, for every even l ranging from 4 to 2 n − 2|F v |; if n ≥ 2 is even then there is a fault-free cycle of length l in F Q n containing e, for every odd l ranging from n + 1 to 2 n − 2|F v | − 1.

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Cycles embedding in folded hypercubes with conditionally faulty vertices

Kuo

Cheng

2017

Discrete Applied Mathematics

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Pancyclicity and bipancyclicity of folded hypercubes with both vertex and edge faults

Cited by 11 publications

References 23 publications

Cycle Embedding in Enhanced Hypercubes with Faulty Vertices

Cycle Embedding in Enhanced Hypercubes with Faulty Vertices

Edge-pancyclicity and edge-bipancyclicity of faulty folded hypercubes

Cycles embedding in folded hypercubes with conditionally faulty vertices

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