2-Disjoint-path-coverable panconnectedness of crossed cubes
Abstract The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respect...
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| Autor*in: |
Chen, Hon-Chan [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2015 |
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| Übergeordnetes Werk: |
Enthalten in: The journal of supercomputing - Springer US, 1987, 71(2015), 7 vom: 03. Apr., Seite 2767-2782 |
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| Übergeordnetes Werk: |
volume:71 ; year:2015 ; number:7 ; day:03 ; month:04 ; pages:2767-2782 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11227-015-1417-9 |
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OLC203394736X |
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| 520 | |a Abstract The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph $$G$$ to be $$2$$-disjoint-path-coverably $$r$$-panconnected for a positive integer $$r$$ if for any four distinct vertices $$u,\, v,\, x$$, and $$y$$ of $$G$$, there exist two vertex-disjoint paths $$P_1$$ and $$P_2,$$ such that (i) $$P_1$$ joins $$u$$ and $$v$$ with length $$l$$ for any integer $$l$$ satisfying $$r \le l \le |V(G)| - r - 2$$, and (ii) $$P_2$$ joins $$x$$ and $$y$$ with length $$|V(G)| - l - 2$$, where $$|V(G)|$$ is the total number of vertices in $$G$$. This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the $$n$$-dimensional crossed cube is $$2$$-disjoint-path-coverably $$n$$-panconnected. | ||
| 650 | 4 | |a Disjoint path cover | |
| 650 | 4 | |a Panconnectedness | |
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| 700 | 1 | |a Hsu, Li-Yen |4 aut | |
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10.1007/s11227-015-1417-9 doi (DE-627)OLC203394736X (DE-He213)s11227-015-1417-9-p DE-627 ger DE-627 rakwb eng 004 620 VZ Chen, Hon-Chan verfasserin aut 2-Disjoint-path-coverable panconnectedness of crossed cubes 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2015 Abstract The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph $$G$$ to be $$2$$-disjoint-path-coverably $$r$$-panconnected for a positive integer $$r$$ if for any four distinct vertices $$u,\, v,\, x$$, and $$y$$ of $$G$$, there exist two vertex-disjoint paths $$P_1$$ and $$P_2,$$ such that (i) $$P_1$$ joins $$u$$ and $$v$$ with length $$l$$ for any integer $$l$$ satisfying $$r \le l \le |V(G)| - r - 2$$, and (ii) $$P_2$$ joins $$x$$ and $$y$$ with length $$|V(G)| - l - 2$$, where $$|V(G)|$$ is the total number of vertices in $$G$$. This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the $$n$$-dimensional crossed cube is $$2$$-disjoint-path-coverably $$n$$-panconnected. Disjoint path cover Panconnectedness Connectivity Crossed cube Interconnection network Kung, Tzu-Liang aut Hsu, Li-Yen aut Enthalten in The journal of supercomputing Springer US, 1987 71(2015), 7 vom: 03. Apr., Seite 2767-2782 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:71 year:2015 number:7 day:03 month:04 pages:2767-2782 https://doi.org/10.1007/s11227-015-1417-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 71 2015 7 03 04 2767-2782 |
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10.1007/s11227-015-1417-9 doi (DE-627)OLC203394736X (DE-He213)s11227-015-1417-9-p DE-627 ger DE-627 rakwb eng 004 620 VZ Chen, Hon-Chan verfasserin aut 2-Disjoint-path-coverable panconnectedness of crossed cubes 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2015 Abstract The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph $$G$$ to be $$2$$-disjoint-path-coverably $$r$$-panconnected for a positive integer $$r$$ if for any four distinct vertices $$u,\, v,\, x$$, and $$y$$ of $$G$$, there exist two vertex-disjoint paths $$P_1$$ and $$P_2,$$ such that (i) $$P_1$$ joins $$u$$ and $$v$$ with length $$l$$ for any integer $$l$$ satisfying $$r \le l \le |V(G)| - r - 2$$, and (ii) $$P_2$$ joins $$x$$ and $$y$$ with length $$|V(G)| - l - 2$$, where $$|V(G)|$$ is the total number of vertices in $$G$$. This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the $$n$$-dimensional crossed cube is $$2$$-disjoint-path-coverably $$n$$-panconnected. Disjoint path cover Panconnectedness Connectivity Crossed cube Interconnection network Kung, Tzu-Liang aut Hsu, Li-Yen aut Enthalten in The journal of supercomputing Springer US, 1987 71(2015), 7 vom: 03. Apr., Seite 2767-2782 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:71 year:2015 number:7 day:03 month:04 pages:2767-2782 https://doi.org/10.1007/s11227-015-1417-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 71 2015 7 03 04 2767-2782 |
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10.1007/s11227-015-1417-9 doi (DE-627)OLC203394736X (DE-He213)s11227-015-1417-9-p DE-627 ger DE-627 rakwb eng 004 620 VZ Chen, Hon-Chan verfasserin aut 2-Disjoint-path-coverable panconnectedness of crossed cubes 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2015 Abstract The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph $$G$$ to be $$2$$-disjoint-path-coverably $$r$$-panconnected for a positive integer $$r$$ if for any four distinct vertices $$u,\, v,\, x$$, and $$y$$ of $$G$$, there exist two vertex-disjoint paths $$P_1$$ and $$P_2,$$ such that (i) $$P_1$$ joins $$u$$ and $$v$$ with length $$l$$ for any integer $$l$$ satisfying $$r \le l \le |V(G)| - r - 2$$, and (ii) $$P_2$$ joins $$x$$ and $$y$$ with length $$|V(G)| - l - 2$$, where $$|V(G)|$$ is the total number of vertices in $$G$$. This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the $$n$$-dimensional crossed cube is $$2$$-disjoint-path-coverably $$n$$-panconnected. Disjoint path cover Panconnectedness Connectivity Crossed cube Interconnection network Kung, Tzu-Liang aut Hsu, Li-Yen aut Enthalten in The journal of supercomputing Springer US, 1987 71(2015), 7 vom: 03. Apr., Seite 2767-2782 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:71 year:2015 number:7 day:03 month:04 pages:2767-2782 https://doi.org/10.1007/s11227-015-1417-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 71 2015 7 03 04 2767-2782 |
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10.1007/s11227-015-1417-9 doi (DE-627)OLC203394736X (DE-He213)s11227-015-1417-9-p DE-627 ger DE-627 rakwb eng 004 620 VZ Chen, Hon-Chan verfasserin aut 2-Disjoint-path-coverable panconnectedness of crossed cubes 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2015 Abstract The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph $$G$$ to be $$2$$-disjoint-path-coverably $$r$$-panconnected for a positive integer $$r$$ if for any four distinct vertices $$u,\, v,\, x$$, and $$y$$ of $$G$$, there exist two vertex-disjoint paths $$P_1$$ and $$P_2,$$ such that (i) $$P_1$$ joins $$u$$ and $$v$$ with length $$l$$ for any integer $$l$$ satisfying $$r \le l \le |V(G)| - r - 2$$, and (ii) $$P_2$$ joins $$x$$ and $$y$$ with length $$|V(G)| - l - 2$$, where $$|V(G)|$$ is the total number of vertices in $$G$$. This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the $$n$$-dimensional crossed cube is $$2$$-disjoint-path-coverably $$n$$-panconnected. Disjoint path cover Panconnectedness Connectivity Crossed cube Interconnection network Kung, Tzu-Liang aut Hsu, Li-Yen aut Enthalten in The journal of supercomputing Springer US, 1987 71(2015), 7 vom: 03. Apr., Seite 2767-2782 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:71 year:2015 number:7 day:03 month:04 pages:2767-2782 https://doi.org/10.1007/s11227-015-1417-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 71 2015 7 03 04 2767-2782 |
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2-Disjoint-path-coverable panconnectedness of crossed cubes |
| abstract |
Abstract The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph $$G$$ to be $$2$$-disjoint-path-coverably $$r$$-panconnected for a positive integer $$r$$ if for any four distinct vertices $$u,\, v,\, x$$, and $$y$$ of $$G$$, there exist two vertex-disjoint paths $$P_1$$ and $$P_2,$$ such that (i) $$P_1$$ joins $$u$$ and $$v$$ with length $$l$$ for any integer $$l$$ satisfying $$r \le l \le |V(G)| - r - 2$$, and (ii) $$P_2$$ joins $$x$$ and $$y$$ with length $$|V(G)| - l - 2$$, where $$|V(G)|$$ is the total number of vertices in $$G$$. This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the $$n$$-dimensional crossed cube is $$2$$-disjoint-path-coverably $$n$$-panconnected. © Springer Science+Business Media New York 2015 |
| abstractGer |
Abstract The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph $$G$$ to be $$2$$-disjoint-path-coverably $$r$$-panconnected for a positive integer $$r$$ if for any four distinct vertices $$u,\, v,\, x$$, and $$y$$ of $$G$$, there exist two vertex-disjoint paths $$P_1$$ and $$P_2,$$ such that (i) $$P_1$$ joins $$u$$ and $$v$$ with length $$l$$ for any integer $$l$$ satisfying $$r \le l \le |V(G)| - r - 2$$, and (ii) $$P_2$$ joins $$x$$ and $$y$$ with length $$|V(G)| - l - 2$$, where $$|V(G)|$$ is the total number of vertices in $$G$$. This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the $$n$$-dimensional crossed cube is $$2$$-disjoint-path-coverably $$n$$-panconnected. © Springer Science+Business Media New York 2015 |
| abstract_unstemmed |
Abstract The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph $$G$$ to be $$2$$-disjoint-path-coverably $$r$$-panconnected for a positive integer $$r$$ if for any four distinct vertices $$u,\, v,\, x$$, and $$y$$ of $$G$$, there exist two vertex-disjoint paths $$P_1$$ and $$P_2,$$ such that (i) $$P_1$$ joins $$u$$ and $$v$$ with length $$l$$ for any integer $$l$$ satisfying $$r \le l \le |V(G)| - r - 2$$, and (ii) $$P_2$$ joins $$x$$ and $$y$$ with length $$|V(G)| - l - 2$$, where $$|V(G)|$$ is the total number of vertices in $$G$$. This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the $$n$$-dimensional crossed cube is $$2$$-disjoint-path-coverably $$n$$-panconnected. © Springer Science+Business Media New York 2015 |
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| title_short |
2-Disjoint-path-coverable panconnectedness of crossed cubes |
| url |
https://doi.org/10.1007/s11227-015-1417-9 |
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| author2 |
Kung, Tzu-Liang Hsu, Li-Yen |
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Kung, Tzu-Liang Hsu, Li-Yen |
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| doi_str |
10.1007/s11227-015-1417-9 |
| up_date |
2024-07-03T19:01:34.919Z |
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