The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs

A vertex <i<w</i< of a connected graph <i<G</i< strongly resolves two distinct vertices <inline-formula<<math display="inline"<<semantics<<mrow<<mi<u</mi<<mo<,</mo<<mi<v</mi<<mo<∈</mo<<mi<...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Dorota Kuziak [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	strong resolving graph strong metric dimension strong resolving set cactus graphs unicyclic graphs

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 8(2020), 8, p 1266
Übergeordnetes Werk:	volume:8 ; year:2020 ; number:8, p 1266

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math8081266

Katalog-ID:	DOAJ008857164

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spelling	10.3390/math8081266 doi (DE-627)DOAJ008857164 (DE-599)DOAJ0613a1a7728148fc811377e4ad38bf20 DE-627 ger DE-627 rakwb eng QA1-939 Dorota Kuziak verfasserin aut The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A vertex <i<w</i< of a connected graph <i<G</i< strongly resolves two distinct vertices <inline-formula<<math display="inline"<<semantics<<mrow<<mi<u</mi<<mo<,</mo<<mi<v</mi<<mo<∈</mo<<mi<V</mi<<mo<(</mo<<mi<G</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, if there is a shortest <inline-formula<<math display="inline"<<semantics<<mrow<<mi<u</mi<<mo<,</mo<<mi<w</mi<</mrow<</semantics<</math<</inline-formula< path containing <i<v</i<, or a shortest <inline-formula<<math display="inline"<<semantics<<mrow<<mi<v</mi<<mo<,</mo<<mi<w</mi<</mrow<</semantics<</math<</inline-formula< path containing <i<u</i<. A set <i<S</i< of vertices of <i<G</i< is a <i<strong resolving set</i< for <i<G</i< if every two distinct vertices of <i<G</i< are strongly resolved by a vertex of <i<S</i<. The smallest cardinality of a strong resolving set for <i<G</i< is called the <i<strong metric dimension</i< of <i<G</i<. To study the strong metric dimension of graphs, a very important role is played by a structure of graphs called the strong resolving graph In this work, we obtain the strong metric dimension of some families of cactus graphs, and along the way, we give several structural properties of the strong resolving graphs of the studied families of cactus graphs. strong resolving graph strong metric dimension strong resolving set cactus graphs unicyclic graphs Mathematics In Mathematics MDPI AG, 2013 8(2020), 8, p 1266 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:8 year:2020 number:8, p 1266 https://doi.org/10.3390/math8081266 kostenfrei https://doaj.org/article/0613a1a7728148fc811377e4ad38bf20 kostenfrei https://www.mdpi.com/2227-7390/8/8/1266 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2020 8, p 1266
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callnumber-first	Q - Science
author	Dorota Kuziak
spellingShingle	Dorota Kuziak misc QA1-939 misc strong resolving graph misc strong metric dimension misc strong resolving set misc cactus graphs misc unicyclic graphs misc Mathematics The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs
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topic_title	QA1-939 The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs strong resolving graph strong metric dimension strong resolving set cactus graphs unicyclic graphs
topic	misc QA1-939 misc strong resolving graph misc strong metric dimension misc strong resolving set misc cactus graphs misc unicyclic graphs misc Mathematics
topic_unstemmed	misc QA1-939 misc strong resolving graph misc strong metric dimension misc strong resolving set misc cactus graphs misc unicyclic graphs misc Mathematics
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title	The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs
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title_full	The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs
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title_sort	strong resolving graph and the strong metric dimension of cactus graphs
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title_auth	The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs
abstract	A vertex <i<w</i< of a connected graph <i<G</i< strongly resolves two distinct vertices <inline-formula<<math display="inline"<<semantics<<mrow<<mi<u</mi<<mo<,</mo<<mi<v</mi<<mo<∈</mo<<mi<V</mi<<mo<(</mo<<mi<G</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, if there is a shortest <inline-formula<<math display="inline"<<semantics<<mrow<<mi<u</mi<<mo<,</mo<<mi<w</mi<</mrow<</semantics<</math<</inline-formula< path containing <i<v</i<, or a shortest <inline-formula<<math display="inline"<<semantics<<mrow<<mi<v</mi<<mo<,</mo<<mi<w</mi<</mrow<</semantics<</math<</inline-formula< path containing <i<u</i<. A set <i<S</i< of vertices of <i<G</i< is a <i<strong resolving set</i< for <i<G</i< if every two distinct vertices of <i<G</i< are strongly resolved by a vertex of <i<S</i<. The smallest cardinality of a strong resolving set for <i<G</i< is called the <i<strong metric dimension</i< of <i<G</i<. To study the strong metric dimension of graphs, a very important role is played by a structure of graphs called the strong resolving graph In this work, we obtain the strong metric dimension of some families of cactus graphs, and along the way, we give several structural properties of the strong resolving graphs of the studied families of cactus graphs.
abstractGer	A vertex <i<w</i< of a connected graph <i<G</i< strongly resolves two distinct vertices <inline-formula<<math display="inline"<<semantics<<mrow<<mi<u</mi<<mo<,</mo<<mi<v</mi<<mo<∈</mo<<mi<V</mi<<mo<(</mo<<mi<G</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, if there is a shortest <inline-formula<<math display="inline"<<semantics<<mrow<<mi<u</mi<<mo<,</mo<<mi<w</mi<</mrow<</semantics<</math<</inline-formula< path containing <i<v</i<, or a shortest <inline-formula<<math display="inline"<<semantics<<mrow<<mi<v</mi<<mo<,</mo<<mi<w</mi<</mrow<</semantics<</math<</inline-formula< path containing <i<u</i<. A set <i<S</i< of vertices of <i<G</i< is a <i<strong resolving set</i< for <i<G</i< if every two distinct vertices of <i<G</i< are strongly resolved by a vertex of <i<S</i<. The smallest cardinality of a strong resolving set for <i<G</i< is called the <i<strong metric dimension</i< of <i<G</i<. To study the strong metric dimension of graphs, a very important role is played by a structure of graphs called the strong resolving graph In this work, we obtain the strong metric dimension of some families of cactus graphs, and along the way, we give several structural properties of the strong resolving graphs of the studied families of cactus graphs.
abstract_unstemmed	A vertex <i<w</i< of a connected graph <i<G</i< strongly resolves two distinct vertices <inline-formula<<math display="inline"<<semantics<<mrow<<mi<u</mi<<mo<,</mo<<mi<v</mi<<mo<∈</mo<<mi<V</mi<<mo<(</mo<<mi<G</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, if there is a shortest <inline-formula<<math display="inline"<<semantics<<mrow<<mi<u</mi<<mo<,</mo<<mi<w</mi<</mrow<</semantics<</math<</inline-formula< path containing <i<v</i<, or a shortest <inline-formula<<math display="inline"<<semantics<<mrow<<mi<v</mi<<mo<,</mo<<mi<w</mi<</mrow<</semantics<</math<</inline-formula< path containing <i<u</i<. A set <i<S</i< of vertices of <i<G</i< is a <i<strong resolving set</i< for <i<G</i< if every two distinct vertices of <i<G</i< are strongly resolved by a vertex of <i<S</i<. The smallest cardinality of a strong resolving set for <i<G</i< is called the <i<strong metric dimension</i< of <i<G</i<. To study the strong metric dimension of graphs, a very important role is played by a structure of graphs called the strong resolving graph In this work, we obtain the strong metric dimension of some families of cactus graphs, and along the way, we give several structural properties of the strong resolving graphs of the studied families of cactus graphs.
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title_short	The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs
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To study the strong metric dimension of graphs, a very important role is played by a structure of graphs called the strong resolving graph In this work, we obtain the strong metric dimension of some families of cactus graphs, and along the way, we give several structural properties of the strong resolving graphs of the studied families of cactus graphs.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">strong resolving graph</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">strong metric dimension</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">strong resolving set</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">cactus graphs</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">unicyclic graphs</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield></datafield><datafield tag="773" ind1="0" 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The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs

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