The panpositionable panconnectedness of crossed cubes
Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube i...
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| Autor*in: |
Chen, Hon-Chan [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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| Übergeordnetes Werk: |
Enthalten in: The journal of supercomputing - Springer US, 1987, 74(2018), 6 vom: 08. März, Seite 2638-2655 |
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| Übergeordnetes Werk: |
volume:74 ; year:2018 ; number:6 ; day:08 ; month:03 ; pages:2638-2655 |
| Links: |
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| DOI / URN: |
10.1007/s11227-018-2295-8 |
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OLC2033954781 |
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| 520 | |a Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube is one of the most popular. In this paper, we investigate the panpositionable panconnectedness problem with respect to the crossed cube. A graph G is r-panpositionably panconnected if for any three distinct vertices x, y, z of G and for any integer $$l_1$$ satisfying $$r \le l_1 \le |V(G)| - r - 1$$, there exists a path $$P = [x, P_1, y, P_2, z]$$ in G such that (i) $$P_1$$ joins x and y with $$l(P_1) = l_1$$ and (ii) $$P_2$$ joins y and z with $$l(P_2) = l_2$$ for any integer $$l_2$$ satisfying $$r \le l_2 \le |V(G)| - l_1 - 1$$, where |V(G)| is the total number of vertices in G and $$l(P_1)$$ (respectively, $$l(P_2)$$) is the length of path $$P_1$$ (respectively, $$P_2$$). By mathematical induction, we demonstrate that the n-dimensional crossed cube $$CQ_n$$ is n-panpositionably panconnected. This result indicates that the path embedding of joining x and z with a mediate vertex y in $$CQ_n$$ is extremely flexible. Moreover, applying our result, crossed cube problems such as panpositionable pancyclicity, panpositionably Hamiltonian connectedness, and panpositionable Hamiltonicity can be solved. | ||
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10.1007/s11227-018-2295-8 doi (DE-627)OLC2033954781 (DE-He213)s11227-018-2295-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Chen, Hon-Chan verfasserin (orcid)0000-0003-0342-6317 aut The panpositionable panconnectedness of crossed cubes 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube is one of the most popular. In this paper, we investigate the panpositionable panconnectedness problem with respect to the crossed cube. A graph G is r-panpositionably panconnected if for any three distinct vertices x, y, z of G and for any integer $$l_1$$ satisfying $$r \le l_1 \le |V(G)| - r - 1$$, there exists a path $$P = [x, P_1, y, P_2, z]$$ in G such that (i) $$P_1$$ joins x and y with $$l(P_1) = l_1$$ and (ii) $$P_2$$ joins y and z with $$l(P_2) = l_2$$ for any integer $$l_2$$ satisfying $$r \le l_2 \le |V(G)| - l_1 - 1$$, where |V(G)| is the total number of vertices in G and $$l(P_1)$$ (respectively, $$l(P_2)$$) is the length of path $$P_1$$ (respectively, $$P_2$$). By mathematical induction, we demonstrate that the n-dimensional crossed cube $$CQ_n$$ is n-panpositionably panconnected. This result indicates that the path embedding of joining x and z with a mediate vertex y in $$CQ_n$$ is extremely flexible. Moreover, applying our result, crossed cube problems such as panpositionable pancyclicity, panpositionably Hamiltonian connectedness, and panpositionable Hamiltonicity can be solved. Path embedding Panconnected Crossed cube Interconnection network Enthalten in The journal of supercomputing Springer US, 1987 74(2018), 6 vom: 08. März, Seite 2638-2655 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:74 year:2018 number:6 day:08 month:03 pages:2638-2655 https://doi.org/10.1007/s11227-018-2295-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2018 6 08 03 2638-2655 |
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10.1007/s11227-018-2295-8 doi (DE-627)OLC2033954781 (DE-He213)s11227-018-2295-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Chen, Hon-Chan verfasserin (orcid)0000-0003-0342-6317 aut The panpositionable panconnectedness of crossed cubes 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube is one of the most popular. In this paper, we investigate the panpositionable panconnectedness problem with respect to the crossed cube. A graph G is r-panpositionably panconnected if for any three distinct vertices x, y, z of G and for any integer $$l_1$$ satisfying $$r \le l_1 \le |V(G)| - r - 1$$, there exists a path $$P = [x, P_1, y, P_2, z]$$ in G such that (i) $$P_1$$ joins x and y with $$l(P_1) = l_1$$ and (ii) $$P_2$$ joins y and z with $$l(P_2) = l_2$$ for any integer $$l_2$$ satisfying $$r \le l_2 \le |V(G)| - l_1 - 1$$, where |V(G)| is the total number of vertices in G and $$l(P_1)$$ (respectively, $$l(P_2)$$) is the length of path $$P_1$$ (respectively, $$P_2$$). By mathematical induction, we demonstrate that the n-dimensional crossed cube $$CQ_n$$ is n-panpositionably panconnected. This result indicates that the path embedding of joining x and z with a mediate vertex y in $$CQ_n$$ is extremely flexible. Moreover, applying our result, crossed cube problems such as panpositionable pancyclicity, panpositionably Hamiltonian connectedness, and panpositionable Hamiltonicity can be solved. Path embedding Panconnected Crossed cube Interconnection network Enthalten in The journal of supercomputing Springer US, 1987 74(2018), 6 vom: 08. März, Seite 2638-2655 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:74 year:2018 number:6 day:08 month:03 pages:2638-2655 https://doi.org/10.1007/s11227-018-2295-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2018 6 08 03 2638-2655 |
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10.1007/s11227-018-2295-8 doi (DE-627)OLC2033954781 (DE-He213)s11227-018-2295-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Chen, Hon-Chan verfasserin (orcid)0000-0003-0342-6317 aut The panpositionable panconnectedness of crossed cubes 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube is one of the most popular. In this paper, we investigate the panpositionable panconnectedness problem with respect to the crossed cube. A graph G is r-panpositionably panconnected if for any three distinct vertices x, y, z of G and for any integer $$l_1$$ satisfying $$r \le l_1 \le |V(G)| - r - 1$$, there exists a path $$P = [x, P_1, y, P_2, z]$$ in G such that (i) $$P_1$$ joins x and y with $$l(P_1) = l_1$$ and (ii) $$P_2$$ joins y and z with $$l(P_2) = l_2$$ for any integer $$l_2$$ satisfying $$r \le l_2 \le |V(G)| - l_1 - 1$$, where |V(G)| is the total number of vertices in G and $$l(P_1)$$ (respectively, $$l(P_2)$$) is the length of path $$P_1$$ (respectively, $$P_2$$). By mathematical induction, we demonstrate that the n-dimensional crossed cube $$CQ_n$$ is n-panpositionably panconnected. This result indicates that the path embedding of joining x and z with a mediate vertex y in $$CQ_n$$ is extremely flexible. Moreover, applying our result, crossed cube problems such as panpositionable pancyclicity, panpositionably Hamiltonian connectedness, and panpositionable Hamiltonicity can be solved. Path embedding Panconnected Crossed cube Interconnection network Enthalten in The journal of supercomputing Springer US, 1987 74(2018), 6 vom: 08. März, Seite 2638-2655 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:74 year:2018 number:6 day:08 month:03 pages:2638-2655 https://doi.org/10.1007/s11227-018-2295-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2018 6 08 03 2638-2655 |
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10.1007/s11227-018-2295-8 doi (DE-627)OLC2033954781 (DE-He213)s11227-018-2295-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Chen, Hon-Chan verfasserin (orcid)0000-0003-0342-6317 aut The panpositionable panconnectedness of crossed cubes 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube is one of the most popular. In this paper, we investigate the panpositionable panconnectedness problem with respect to the crossed cube. A graph G is r-panpositionably panconnected if for any three distinct vertices x, y, z of G and for any integer $$l_1$$ satisfying $$r \le l_1 \le |V(G)| - r - 1$$, there exists a path $$P = [x, P_1, y, P_2, z]$$ in G such that (i) $$P_1$$ joins x and y with $$l(P_1) = l_1$$ and (ii) $$P_2$$ joins y and z with $$l(P_2) = l_2$$ for any integer $$l_2$$ satisfying $$r \le l_2 \le |V(G)| - l_1 - 1$$, where |V(G)| is the total number of vertices in G and $$l(P_1)$$ (respectively, $$l(P_2)$$) is the length of path $$P_1$$ (respectively, $$P_2$$). By mathematical induction, we demonstrate that the n-dimensional crossed cube $$CQ_n$$ is n-panpositionably panconnected. This result indicates that the path embedding of joining x and z with a mediate vertex y in $$CQ_n$$ is extremely flexible. Moreover, applying our result, crossed cube problems such as panpositionable pancyclicity, panpositionably Hamiltonian connectedness, and panpositionable Hamiltonicity can be solved. Path embedding Panconnected Crossed cube Interconnection network Enthalten in The journal of supercomputing Springer US, 1987 74(2018), 6 vom: 08. März, Seite 2638-2655 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:74 year:2018 number:6 day:08 month:03 pages:2638-2655 https://doi.org/10.1007/s11227-018-2295-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2018 6 08 03 2638-2655 |
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10.1007/s11227-018-2295-8 doi (DE-627)OLC2033954781 (DE-He213)s11227-018-2295-8-p DE-627 ger DE-627 rakwb eng 004 620 VZ Chen, Hon-Chan verfasserin (orcid)0000-0003-0342-6317 aut The panpositionable panconnectedness of crossed cubes 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube is one of the most popular. In this paper, we investigate the panpositionable panconnectedness problem with respect to the crossed cube. A graph G is r-panpositionably panconnected if for any three distinct vertices x, y, z of G and for any integer $$l_1$$ satisfying $$r \le l_1 \le |V(G)| - r - 1$$, there exists a path $$P = [x, P_1, y, P_2, z]$$ in G such that (i) $$P_1$$ joins x and y with $$l(P_1) = l_1$$ and (ii) $$P_2$$ joins y and z with $$l(P_2) = l_2$$ for any integer $$l_2$$ satisfying $$r \le l_2 \le |V(G)| - l_1 - 1$$, where |V(G)| is the total number of vertices in G and $$l(P_1)$$ (respectively, $$l(P_2)$$) is the length of path $$P_1$$ (respectively, $$P_2$$). By mathematical induction, we demonstrate that the n-dimensional crossed cube $$CQ_n$$ is n-panpositionably panconnected. This result indicates that the path embedding of joining x and z with a mediate vertex y in $$CQ_n$$ is extremely flexible. Moreover, applying our result, crossed cube problems such as panpositionable pancyclicity, panpositionably Hamiltonian connectedness, and panpositionable Hamiltonicity can be solved. Path embedding Panconnected Crossed cube Interconnection network Enthalten in The journal of supercomputing Springer US, 1987 74(2018), 6 vom: 08. März, Seite 2638-2655 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:74 year:2018 number:6 day:08 month:03 pages:2638-2655 https://doi.org/10.1007/s11227-018-2295-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2018 6 08 03 2638-2655 |
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the panpositionable panconnectedness of crossed cubes |
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The panpositionable panconnectedness of crossed cubes |
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Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube is one of the most popular. In this paper, we investigate the panpositionable panconnectedness problem with respect to the crossed cube. A graph G is r-panpositionably panconnected if for any three distinct vertices x, y, z of G and for any integer $$l_1$$ satisfying $$r \le l_1 \le |V(G)| - r - 1$$, there exists a path $$P = [x, P_1, y, P_2, z]$$ in G such that (i) $$P_1$$ joins x and y with $$l(P_1) = l_1$$ and (ii) $$P_2$$ joins y and z with $$l(P_2) = l_2$$ for any integer $$l_2$$ satisfying $$r \le l_2 \le |V(G)| - l_1 - 1$$, where |V(G)| is the total number of vertices in G and $$l(P_1)$$ (respectively, $$l(P_2)$$) is the length of path $$P_1$$ (respectively, $$P_2$$). By mathematical induction, we demonstrate that the n-dimensional crossed cube $$CQ_n$$ is n-panpositionably panconnected. This result indicates that the path embedding of joining x and z with a mediate vertex y in $$CQ_n$$ is extremely flexible. Moreover, applying our result, crossed cube problems such as panpositionable pancyclicity, panpositionably Hamiltonian connectedness, and panpositionable Hamiltonicity can be solved. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
| abstractGer |
Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube is one of the most popular. In this paper, we investigate the panpositionable panconnectedness problem with respect to the crossed cube. A graph G is r-panpositionably panconnected if for any three distinct vertices x, y, z of G and for any integer $$l_1$$ satisfying $$r \le l_1 \le |V(G)| - r - 1$$, there exists a path $$P = [x, P_1, y, P_2, z]$$ in G such that (i) $$P_1$$ joins x and y with $$l(P_1) = l_1$$ and (ii) $$P_2$$ joins y and z with $$l(P_2) = l_2$$ for any integer $$l_2$$ satisfying $$r \le l_2 \le |V(G)| - l_1 - 1$$, where |V(G)| is the total number of vertices in G and $$l(P_1)$$ (respectively, $$l(P_2)$$) is the length of path $$P_1$$ (respectively, $$P_2$$). By mathematical induction, we demonstrate that the n-dimensional crossed cube $$CQ_n$$ is n-panpositionably panconnected. This result indicates that the path embedding of joining x and z with a mediate vertex y in $$CQ_n$$ is extremely flexible. Moreover, applying our result, crossed cube problems such as panpositionable pancyclicity, panpositionably Hamiltonian connectedness, and panpositionable Hamiltonicity can be solved. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
| abstract_unstemmed |
Abstract In many parallel and distributed multiprocessor systems, the processors are connected based on different types of interconnection networks. The topological structure of an interconnection network is typically modeled as a graph. Among the many kinds of network topologies, the crossed cube is one of the most popular. In this paper, we investigate the panpositionable panconnectedness problem with respect to the crossed cube. A graph G is r-panpositionably panconnected if for any three distinct vertices x, y, z of G and for any integer $$l_1$$ satisfying $$r \le l_1 \le |V(G)| - r - 1$$, there exists a path $$P = [x, P_1, y, P_2, z]$$ in G such that (i) $$P_1$$ joins x and y with $$l(P_1) = l_1$$ and (ii) $$P_2$$ joins y and z with $$l(P_2) = l_2$$ for any integer $$l_2$$ satisfying $$r \le l_2 \le |V(G)| - l_1 - 1$$, where |V(G)| is the total number of vertices in G and $$l(P_1)$$ (respectively, $$l(P_2)$$) is the length of path $$P_1$$ (respectively, $$P_2$$). By mathematical induction, we demonstrate that the n-dimensional crossed cube $$CQ_n$$ is n-panpositionably panconnected. This result indicates that the path embedding of joining x and z with a mediate vertex y in $$CQ_n$$ is extremely flexible. Moreover, applying our result, crossed cube problems such as panpositionable pancyclicity, panpositionably Hamiltonian connectedness, and panpositionable Hamiltonicity can be solved. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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The panpositionable panconnectedness of crossed cubes |
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