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
Autor*in: |
Kuziak, Dorota [verfasserIn] |
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Format: |
E-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 - Berlin : Springer, 1978, 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 |
Links: |
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DOI / URN: |
10.1007/s00025-016-0563-6 |
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Katalog-ID: |
SPR000273279 |
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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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650 | 4 | |a strong metric dimension |7 (dpeaa)DE-He213 | |
650 | 4 | |a direct product of graphs |7 (dpeaa)DE-He213 | |
650 | 4 | |a strong resolving graph |7 (dpeaa)DE-He213 | |
700 | 1 | |a Peterin, Iztok |4 aut | |
700 | 1 | |a Yero, Ismael G. |0 (orcid)0000-0002-1619-1572 |4 aut | |
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10.1007/s00025-016-0563-6 doi (DE-627)SPR000273279 (SPR)s00025-016-0563-6-e DE-627 ger DE-627 rakwb eng Kuziak, Dorota verfasserin aut Resolvability and Strong Resolvability in the Direct Product of Graphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr 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 (dpeaa)DE-He213 strong metric dimension (dpeaa)DE-He213 direct product of graphs (dpeaa)DE-He213 strong resolving graph (dpeaa)DE-He213 Peterin, Iztok aut Yero, Ismael G. (orcid)0000-0002-1619-1572 aut Enthalten in Results in mathematics Berlin : Springer, 1978 71(2016), 1-2 vom: 21. Juni, Seite 509-526 (DE-627)327046066 (DE-600)2043519-8 1420-9012 nnns volume:71 year:2016 number:1-2 day:21 month:06 pages:509-526 https://dx.doi.org/10.1007/s00025-016-0563-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 71 2016 1-2 21 06 509-526 |
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10.1007/s00025-016-0563-6 doi (DE-627)SPR000273279 (SPR)s00025-016-0563-6-e DE-627 ger DE-627 rakwb eng Kuziak, Dorota verfasserin aut Resolvability and Strong Resolvability in the Direct Product of Graphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr 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 (dpeaa)DE-He213 strong metric dimension (dpeaa)DE-He213 direct product of graphs (dpeaa)DE-He213 strong resolving graph (dpeaa)DE-He213 Peterin, Iztok aut Yero, Ismael G. (orcid)0000-0002-1619-1572 aut Enthalten in Results in mathematics Berlin : Springer, 1978 71(2016), 1-2 vom: 21. Juni, Seite 509-526 (DE-627)327046066 (DE-600)2043519-8 1420-9012 nnns volume:71 year:2016 number:1-2 day:21 month:06 pages:509-526 https://dx.doi.org/10.1007/s00025-016-0563-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 71 2016 1-2 21 06 509-526 |
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10.1007/s00025-016-0563-6 doi (DE-627)SPR000273279 (SPR)s00025-016-0563-6-e DE-627 ger DE-627 rakwb eng Kuziak, Dorota verfasserin aut Resolvability and Strong Resolvability in the Direct Product of Graphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr 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 (dpeaa)DE-He213 strong metric dimension (dpeaa)DE-He213 direct product of graphs (dpeaa)DE-He213 strong resolving graph (dpeaa)DE-He213 Peterin, Iztok aut Yero, Ismael G. (orcid)0000-0002-1619-1572 aut Enthalten in Results in mathematics Berlin : Springer, 1978 71(2016), 1-2 vom: 21. Juni, Seite 509-526 (DE-627)327046066 (DE-600)2043519-8 1420-9012 nnns volume:71 year:2016 number:1-2 day:21 month:06 pages:509-526 https://dx.doi.org/10.1007/s00025-016-0563-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 71 2016 1-2 21 06 509-526 |
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10.1007/s00025-016-0563-6 doi (DE-627)SPR000273279 (SPR)s00025-016-0563-6-e DE-627 ger DE-627 rakwb eng Kuziak, Dorota verfasserin aut Resolvability and Strong Resolvability in the Direct Product of Graphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr 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 (dpeaa)DE-He213 strong metric dimension (dpeaa)DE-He213 direct product of graphs (dpeaa)DE-He213 strong resolving graph (dpeaa)DE-He213 Peterin, Iztok aut Yero, Ismael G. (orcid)0000-0002-1619-1572 aut Enthalten in Results in mathematics Berlin : Springer, 1978 71(2016), 1-2 vom: 21. Juni, Seite 509-526 (DE-627)327046066 (DE-600)2043519-8 1420-9012 nnns volume:71 year:2016 number:1-2 day:21 month:06 pages:509-526 https://dx.doi.org/10.1007/s00025-016-0563-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 71 2016 1-2 21 06 509-526 |
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10.1007/s00025-016-0563-6 doi (DE-627)SPR000273279 (SPR)s00025-016-0563-6-e DE-627 ger DE-627 rakwb eng Kuziak, Dorota verfasserin aut Resolvability and Strong Resolvability in the Direct Product of Graphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr 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 (dpeaa)DE-He213 strong metric dimension (dpeaa)DE-He213 direct product of graphs (dpeaa)DE-He213 strong resolving graph (dpeaa)DE-He213 Peterin, Iztok aut Yero, Ismael G. (orcid)0000-0002-1619-1572 aut Enthalten in Results in mathematics Berlin : Springer, 1978 71(2016), 1-2 vom: 21. Juni, Seite 509-526 (DE-627)327046066 (DE-600)2043519-8 1420-9012 nnns volume:71 year:2016 number:1-2 day:21 month:06 pages:509-526 https://dx.doi.org/10.1007/s00025-016-0563-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 71 2016 1-2 21 06 509-526 |
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Kuziak, Dorota misc Metric dimension misc strong metric dimension misc direct product of graphs misc strong resolving graph Resolvability and Strong Resolvability in the Direct Product of Graphs |
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Resolvability and Strong Resolvability in the Direct Product of Graphs Metric dimension (dpeaa)DE-He213 strong metric dimension (dpeaa)DE-He213 direct product of graphs (dpeaa)DE-He213 strong resolving graph (dpeaa)DE-He213 |
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resolvability and strong resolvability in the direct product of graphs |
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Resolvability and Strong Resolvability in the Direct Product of Graphs |
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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 |
abstractGer |
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 |
abstract_unstemmed |
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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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. 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