Paired and semipaired domination in near-triangulations
A dominating set of a graph G is a subset D of vertices such that every vertex not in D is adjacent to at least one vertex in D. A dominating set D is paired if the subgraph induced by its vertices has a perfect matching, and semipaired if every vertex in D is paired with exactly one other vertex in...
| Autores: | , , , , |
|---|---|
| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/374877 |
| Acceso en línea: | https://hdl.handle.net/2117/374877 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Grafs, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | A dominating set of a graph G is a subset D of vertices such that every vertex not in D is adjacent to at least one vertex in D. A dominating set D is paired if the subgraph induced by its vertices has a perfect matching, and semipaired if every vertex in D is paired with exactly one other vertex in D that is within distance 2 from it. The paired domination number, denoted by ¿pr(G), is the minimum cardinality of a paired dominating set of G, and the semipaired domination number, denoted by ¿pr2(G), is the minimum cardinality of a semipaired dominating set of G. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that ¿pr(G) = 2b n 4 c for any neartriangulation G of order n = 4, and that with some exceptions, ¿pr2(G) = b 2n 5 c for any near-triangulation G of order n = 5. |
|---|