Edge-pancyclicity of twisted cubes

Jianxi Fan; Xiaola Lin; Xiaohua Jia; Rynson W. H. Lau

doi:10.1007/11602613_108

Edge-pancyclicity of twisted cubes

Jianxi Fan
, Xiaola Lin
, Xiaohua Jia
, Rynson W. H. Lau

Department of Computer Science

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

35 Citations (Scopus)

Abstract

Twisted cubes are attractive alternatives to hypercubes. In this paper, we study a stronger pancyclicity of twisted cubes. We prove that the n-dimensional twisted cube is edge-pancyclic for n ≥ 3. That is, for any (x, y) ∈ E(TQ_n)(n ≥ 3) and any integer l with 4 ≤ l ≤ 2ⁿ, a cycle C of length l can be embedded with dilation 1 into TQ_n such that (x, y) is in C. It is clear that an edge-pancyclic graph is also a node-pancyclic graph. Therefore, TQ_n is also a node-pancyclic graph for n ≥ 3. © Springer-Verlag Berlin Heidelberg 2005.

Original language	English
Title of host publication	Algorithms and Computation
Subtitle of host publication	16th International Symposium, ISAAC 2005, Proceedings
Publisher	Springer Verlag
Pages	1090-1099
Volume	3827 LNCS
ISBN (Print)	3540309357, 9783540309352
DOIs	https://doi.org/10.1007/11602613_108
Publication status	Published - 2005
Event	16th International Symposium on Algorithms and Computation (ISAAC 2005) - Hainan, China Duration: 19 Dec 2005 → 21 Dec 2005

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3827 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th International Symposium on Algorithms and Computation (ISAAC 2005)
Place	China
City	Hainan
Period	19/12/05 → 21/12/05

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Fan, J., Lin, X., Jia, X., & Lau, R. W. H. (2005). Edge-pancyclicity of twisted cubes. In Algorithms and Computation: 16th International Symposium, ISAAC 2005, Proceedings (Vol. 3827 LNCS, pp. 1090-1099). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS). Springer Verlag. https://doi.org/10.1007/11602613_108

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title = "Edge-pancyclicity of twisted cubes",

abstract = "Twisted cubes are attractive alternatives to hypercubes. In this paper, we study a stronger pancyclicity of twisted cubes. We prove that the n-dimensional twisted cube is edge-pancyclic for n ≥ 3. That is, for any (x, y) ∈ E(TQn)(n ≥ 3) and any integer l with 4 ≤ l ≤ 2n, a cycle C of length l can be embedded with dilation 1 into TQn such that (x, y) is in C. It is clear that an edge-pancyclic graph is also a node-pancyclic graph. Therefore, TQn is also a node-pancyclic graph for n ≥ 3. {\textcopyright} Springer-Verlag Berlin Heidelberg 2005.",

author = "Jianxi Fan and Xiaola Lin and Xiaohua Jia and Lau, \{Rynson W. H.\}",

year = "2005",

doi = "10.1007/11602613\_108",

language = "English",

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volume = "3827 LNCS",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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pages = "1090--1099",

booktitle = "Algorithms and Computation",

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note = "16th International Symposium on Algorithms and Computation (ISAAC 2005) ; Conference date: 19-12-2005 Through 21-12-2005",

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Fan, J, Lin, X, Jia, X & Lau, RWH 2005, Edge-pancyclicity of twisted cubes. in Algorithms and Computation: 16th International Symposium, ISAAC 2005, Proceedings. vol. 3827 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3827 LNCS, Springer Verlag, pp. 1090-1099, 16th International Symposium on Algorithms and Computation (ISAAC 2005), Hainan, China, 19/12/05. https://doi.org/10.1007/11602613_108

Edge-pancyclicity of twisted cubes. / Fan, Jianxi; Lin, Xiaola; Jia, Xiaohua et al.
Algorithms and Computation: 16th International Symposium, ISAAC 2005, Proceedings. Vol. 3827 LNCS Springer Verlag, 2005. p. 1090-1099 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Edge-pancyclicity of twisted cubes

AU - Fan, Jianxi

AU - Lin, Xiaola

AU - Jia, Xiaohua

AU - Lau, Rynson W. H.

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N2 - Twisted cubes are attractive alternatives to hypercubes. In this paper, we study a stronger pancyclicity of twisted cubes. We prove that the n-dimensional twisted cube is edge-pancyclic for n ≥ 3. That is, for any (x, y) ∈ E(TQn)(n ≥ 3) and any integer l with 4 ≤ l ≤ 2n, a cycle C of length l can be embedded with dilation 1 into TQn such that (x, y) is in C. It is clear that an edge-pancyclic graph is also a node-pancyclic graph. Therefore, TQn is also a node-pancyclic graph for n ≥ 3. © Springer-Verlag Berlin Heidelberg 2005.

AB - Twisted cubes are attractive alternatives to hypercubes. In this paper, we study a stronger pancyclicity of twisted cubes. We prove that the n-dimensional twisted cube is edge-pancyclic for n ≥ 3. That is, for any (x, y) ∈ E(TQn)(n ≥ 3) and any integer l with 4 ≤ l ≤ 2n, a cycle C of length l can be embedded with dilation 1 into TQn such that (x, y) is in C. It is clear that an edge-pancyclic graph is also a node-pancyclic graph. Therefore, TQn is also a node-pancyclic graph for n ≥ 3. © Springer-Verlag Berlin Heidelberg 2005.

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DO - 10.1007/11602613_108

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 3540309357

SN - 9783540309352

VL - 3827 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Algorithms and Computation

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T2 - 16th International Symposium on Algorithms and Computation (ISAAC 2005)

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ER -

Edge-pancyclicity of twisted cubes

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