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>&...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/52b519f0fcfa4350a196197c6637ae8f |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | 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. |
|---|