The <i>k</i>-Metric Dimension of a Unicyclic Graph

Given a connected graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>(</mo><mi>G</mi>&...

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Autor principal:	Alejandro Estrada-Moreno
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	unicyclic graph <i>k</i>-metric generator <i>k</i>-metric dimension <i>k</i>-metric dimensional graph linear programming problem Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/52b519f0fcfa4350a196197c6637ae8f
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spelling	oai:doaj.org-article:52b519f0fcfa4350a196197c6637ae8f2021-11-11T18:19:36ZThe <i>k</i>-Metric Dimension of a Unicyclic Graph10.3390/math92127892227-7390https://doaj.org/article/52b519f0fcfa4350a196197c6637ae8f2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2789https://doaj.org/toc/2227-7390Given a connected graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></mrow></semantics></math></inline-formula>, a set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> is said to be a <i>k</i>-metric generator for <i>G</i> if any pair of different vertices in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> is distinguished by at least <i>k</i> elements of <i>S</i>. A metric generator of minimum cardinality among all <i>k</i>-metric generators is called a <i>k</i>-metric basis and its cardinality is the <i>k</i>-metric dimension of <i>G</i>. We initially present a linear programming problem that describes the problem of finding the <i>k</i>-metric dimension and a <i>k</i>-metric basis of a graph <i>G</i>. Then we conducted a study on the k-metric dimension of a unicyclic graph.Alejandro Estrada-MorenoMDPI AGarticleunicyclic graph<i>k</i>-metric generator<i>k</i>-metric dimension<i>k</i>-metric dimensional graphlinear programming problemMathematicsQA1-939ENMathematics, Vol 9, Iss 2789, p 2789 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	unicyclic graph <i>k</i>-metric generator <i>k</i>-metric dimension <i>k</i>-metric dimensional graph linear programming problem Mathematics QA1-939
spellingShingle	unicyclic graph <i>k</i>-metric generator <i>k</i>-metric dimension <i>k</i>-metric dimensional graph linear programming problem Mathematics QA1-939 Alejandro Estrada-Moreno The <i>k</i>-Metric Dimension of a Unicyclic Graph
description	Given a connected graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></mrow></semantics></math></inline-formula>, a set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> is said to be a <i>k</i>-metric generator for <i>G</i> if any pair of different vertices in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> is distinguished by at least <i>k</i> elements of <i>S</i>. A metric generator of minimum cardinality among all <i>k</i>-metric generators is called a <i>k</i>-metric basis and its cardinality is the <i>k</i>-metric dimension of <i>G</i>. We initially present a linear programming problem that describes the problem of finding the <i>k</i>-metric dimension and a <i>k</i>-metric basis of a graph <i>G</i>. Then we conducted a study on the k-metric dimension of a unicyclic graph.
format	article
author	Alejandro Estrada-Moreno
author_facet	Alejandro Estrada-Moreno
author_sort	Alejandro Estrada-Moreno
title	The <i>k</i>-Metric Dimension of a Unicyclic Graph
title_short	The <i>k</i>-Metric Dimension of a Unicyclic Graph
title_full	The <i>k</i>-Metric Dimension of a Unicyclic Graph
title_fullStr	The <i>k</i>-Metric Dimension of a Unicyclic Graph
title_full_unstemmed	The <i>k</i>-Metric Dimension of a Unicyclic Graph
title_sort	<i>k</i>-metric dimension of a unicyclic graph
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/52b519f0fcfa4350a196197c6637ae8f
work_keys_str_mv	AT alejandroestradamoreno theikimetricdimensionofaunicyclicgraph AT alejandroestradamoreno ikimetricdimensionofaunicyclicgraph
_version_	1718431883980701696

The <i>k</i>-Metric Dimension of a Unicyclic Graph

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