Resolvability and Strong Resolvability in the Direct Product of Graphs
Abstract Given a connected graph G, a vertex $${w \in V(G)}$$ distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kuziak, Dorota [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer International Publishing 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Results in mathematics - Springer International Publishing, 1984, 71(2016), 1-2 vom: 21. Juni, Seite 509-526 |
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| Übergeordnetes Werk: |
volume:71 ; year:2016 ; number:1-2 ; day:21 ; month:06 ; pages:509-526 |
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| DOI / URN: |
10.1007/s00025-016-0563-6 |
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| 520 | |a Abstract Given a connected graph G, a vertex $${w \in V(G)}$$ distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs. | ||
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10.1007/s00025-016-0563-6 doi (DE-627)OLC2069535703 (DE-He213)s00025-016-0563-6-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Kuziak, Dorota verfasserin aut Resolvability and Strong Resolvability in the Direct Product of Graphs 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract Given a connected graph G, a vertex $${w \in V(G)}$$ distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs. Metric dimension strong metric dimension direct product of graphs strong resolving graph Peterin, Iztok aut Yero, Ismael G. (orcid)0000-0002-1619-1572 aut Enthalten in Results in mathematics Springer International Publishing, 1984 71(2016), 1-2 vom: 21. Juni, Seite 509-526 (DE-627)129571423 (DE-600)226632-5 (DE-576)015060160 1422-6383 nnns volume:71 year:2016 number:1-2 day:21 month:06 pages:509-526 https://doi.org/10.1007/s00025-016-0563-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4277 GBV_ILN_4318 AR 71 2016 1-2 21 06 509-526 |
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10.1007/s00025-016-0563-6 doi (DE-627)OLC2069535703 (DE-He213)s00025-016-0563-6-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Kuziak, Dorota verfasserin aut Resolvability and Strong Resolvability in the Direct Product of Graphs 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract Given a connected graph G, a vertex $${w \in V(G)}$$ distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs. Metric dimension strong metric dimension direct product of graphs strong resolving graph Peterin, Iztok aut Yero, Ismael G. (orcid)0000-0002-1619-1572 aut Enthalten in Results in mathematics Springer International Publishing, 1984 71(2016), 1-2 vom: 21. Juni, Seite 509-526 (DE-627)129571423 (DE-600)226632-5 (DE-576)015060160 1422-6383 nnns volume:71 year:2016 number:1-2 day:21 month:06 pages:509-526 https://doi.org/10.1007/s00025-016-0563-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4277 GBV_ILN_4318 AR 71 2016 1-2 21 06 509-526 |
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10.1007/s00025-016-0563-6 doi (DE-627)OLC2069535703 (DE-He213)s00025-016-0563-6-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Kuziak, Dorota verfasserin aut Resolvability and Strong Resolvability in the Direct Product of Graphs 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract Given a connected graph G, a vertex $${w \in V(G)}$$ distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs. Metric dimension strong metric dimension direct product of graphs strong resolving graph Peterin, Iztok aut Yero, Ismael G. (orcid)0000-0002-1619-1572 aut Enthalten in Results in mathematics Springer International Publishing, 1984 71(2016), 1-2 vom: 21. Juni, Seite 509-526 (DE-627)129571423 (DE-600)226632-5 (DE-576)015060160 1422-6383 nnns volume:71 year:2016 number:1-2 day:21 month:06 pages:509-526 https://doi.org/10.1007/s00025-016-0563-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4277 GBV_ILN_4318 AR 71 2016 1-2 21 06 509-526 |
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10.1007/s00025-016-0563-6 doi (DE-627)OLC2069535703 (DE-He213)s00025-016-0563-6-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Kuziak, Dorota verfasserin aut Resolvability and Strong Resolvability in the Direct Product of Graphs 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract Given a connected graph G, a vertex $${w \in V(G)}$$ distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs. Metric dimension strong metric dimension direct product of graphs strong resolving graph Peterin, Iztok aut Yero, Ismael G. (orcid)0000-0002-1619-1572 aut Enthalten in Results in mathematics Springer International Publishing, 1984 71(2016), 1-2 vom: 21. Juni, Seite 509-526 (DE-627)129571423 (DE-600)226632-5 (DE-576)015060160 1422-6383 nnns volume:71 year:2016 number:1-2 day:21 month:06 pages:509-526 https://doi.org/10.1007/s00025-016-0563-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4277 GBV_ILN_4318 AR 71 2016 1-2 21 06 509-526 |
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Abstract Given a connected graph G, a vertex $${w \in V(G)}$$ distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs. © Springer International Publishing 2016 |
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Abstract Given a connected graph G, a vertex $${w \in V(G)}$$ distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs. © Springer International Publishing 2016 |
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Abstract Given a connected graph G, a vertex $${w \in V(G)}$$ distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs. © Springer International Publishing 2016 |
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Resolvability and Strong Resolvability in the Direct Product of Graphs |
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Peterin, Iztok Yero, Ismael G. |
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