Hamiltonian properties of twisted hypercube-like networks with more faulty elements
Twisted hypercube-like networks (THLNs) are a large class of network topologies, which subsume some well-known hypercube variants. This paper is concerned with the longest cycle in an n -dimensional ( n -D) THLN with up to 2 n − 9 faulty elements. Let G be an n -D THLN, n ≥ 7 . Let F be a subset of...
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| Published in | Theoretical computer science Vol. 412; no. 22; pp. 2409 - 2417 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Elsevier B.V
13.05.2011
Elsevier |
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| Abstract | Twisted hypercube-like networks (THLNs) are a large class of network topologies, which subsume some well-known hypercube variants. This paper is concerned with the longest cycle in an
n
-dimensional (
n
-D) THLN with up to
2
n
−
9
faulty elements. Let
G
be an
n
-D THLN,
n
≥
7
. Let
F
be a subset of
V
(
G
)
⋃
E
(
G
)
,
|
F
|
≤
2
n
−
9
. We prove that
G
−
F
contains a Hamiltonian cycle if
δ
(
G
−
F
)
≥
2
, and
G
−
F
contains a near Hamiltonian cycle if
δ
(
G
−
F
)
≤
1
. Our work extends some previously known results. |
|---|---|
| AbstractList | Twisted hypercube-like networks (THLNs) are a large class of network topologies, which subsume some well-known hypercube variants. This paper is concerned with the longest cycle in an
n
-dimensional (
n
-D) THLN with up to
2
n
−
9
faulty elements. Let
G
be an
n
-D THLN,
n
≥
7
. Let
F
be a subset of
V
(
G
)
⋃
E
(
G
)
,
|
F
|
≤
2
n
−
9
. We prove that
G
−
F
contains a Hamiltonian cycle if
δ
(
G
−
F
)
≥
2
, and
G
−
F
contains a near Hamiltonian cycle if
δ
(
G
−
F
)
≤
1
. Our work extends some previously known results. Twisted hypercube-like networks (THLNs) are a large class of network topologies, which subsume some well-known hypercube variants. This paper is concerned with the longest cycle in an n -dimensional ( n -D) THLN with up to 2 n a 9 faulty elements. Let G be an n -D THLN, n aY 7 . Let F be a subset of V ( G ) a E ( G ) , |
| Author | Yang, Erjie Yang, Xiaofan Dong, Qiang Cao, Jianqiu |
| Author_xml | – sequence: 1 givenname: Xiaofan surname: Yang fullname: Yang, Xiaofan email: xf_yang1964@yahoo.com, yxf640126@sina.com organization: College of Computer Science, Chongqing University, Chongqing 400044, China – sequence: 2 givenname: Qiang surname: Dong fullname: Dong, Qiang organization: College of Computer Science, Chongqing University, Chongqing 400044, China – sequence: 3 givenname: Erjie surname: Yang fullname: Yang, Erjie organization: College of Computer Science, Chongqing University, Chongqing 400044, China – sequence: 4 givenname: Jianqiu surname: Cao fullname: Cao, Jianqiu organization: School of Information Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, China |
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| CitedBy_id | crossref_primary_10_1016_j_ins_2014_05_052 crossref_primary_10_1016_j_tcs_2017_12_023 crossref_primary_10_3745_KIPSTA_2011_18A_6_225 crossref_primary_10_1016_j_tcs_2014_09_041 crossref_primary_10_1093_comjnl_bxv019 crossref_primary_10_32604_cmc_2021_016123 crossref_primary_10_1016_j_ins_2013_06_053 crossref_primary_10_1016_j_tcs_2012_11_034 crossref_primary_10_1016_j_jpdc_2011_09_002 crossref_primary_10_1109_ACCESS_2018_2882520 crossref_primary_10_3390_math7111066 |
| Cites_doi | 10.1109/TC.2006.104 10.1007/3-540-17943-7_126 10.1109/71.159036 10.1016/j.parco.2003.12.003 10.1016/j.ins.2008.10.011 10.1002/1097-0037(200012)36:4<225::AID-NET3>3.0.CO;2-G 10.1016/j.ipl.2005.10.003 10.1080/0020716042000301752 10.1109/TPDS.2006.37 10.1093/ietfec/E88-A.1.346 10.1016/j.tcs.2007.02.029 10.1109/TPDS.2008.123 10.1109/71.755822 10.1016/S0096-3003(02)00223-0 10.1109/12.381950 10.1137/090753747 10.1016/j.tcs.2008.06.024 10.1016/j.endm.2009.07.006 10.1109/TC.2005.33 10.1016/j.ipl.2007.10.009 10.1016/j.ipl.2010.04.014 10.1016/j.ipl.2004.03.009 |
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| Keywords | Fault tolerance Near Hamiltonian cycle Twisted hypercube-like network Hamiltonian cycle Interconnection networks Interconnection network Network topology Fault tolerant computing Computer theory Hypercube Hamiltonian |
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Lett. doi: 10.1016/j.ipl.2007.10.009 contributor: fullname: Shih – volume: 110 start-page: 464 issue: 11 year: 2010 ident: 10.1016/j.tcs.2011.01.034_br000020 article-title: Embedding a long fault-free cycle in a crossed cube with more faulty nodes publication-title: Inform. Process. Lett. doi: 10.1016/j.ipl.2010.04.014 contributor: fullname: Dong – volume: 91 start-page: 11 issue: 1 year: 2004 ident: 10.1016/j.tcs.2011.01.034_br000085 article-title: Hamiltonian properties on the class of hypercube-like networks publication-title: Inform. Process. Lett. doi: 10.1016/j.ipl.2004.03.009 contributor: fullname: Park |
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| Snippet | Twisted hypercube-like networks (THLNs) are a large class of network topologies, which subsume some well-known hypercube variants. This paper is concerned with... |
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| SubjectTerms | Applied sciences Computer science; control theory; systems Computer systems performance. Reliability Exact sciences and technology Fault tolerance Hamiltonian cycle Hypercubes Interconnection networks Miscellaneous Near Hamiltonian cycle Networks Software Theoretical computing Topology Twisted hypercube-like network |
| Title | Hamiltonian properties of twisted hypercube-like networks with more faulty elements |
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