Distance 2-domination in prisms of graphs
A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ¿ ( V ( G ) - D ) and D is at most two. Let ¿ 2 ( G ) denote the size of a smallest distance 2 -dominating set of G . For any permutation p of the vertex set of G , the prism of G with respect...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| 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:2117/112675 |
| Acceso en línea: | https://hdl.handle.net/2117/112675 https://dx.doi.org/10.7151/dmgt.1946 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory distance 2-dominating set prisms of graphs universal fixer Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Sumario: | A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ¿ ( V ( G ) - D ) and D is at most two. Let ¿ 2 ( G ) denote the size of a smallest distance 2 -dominating set of G . For any permutation p of the vertex set of G , the prism of G with respect to p is the graph pG obtained from G and a copy G ' of G by joining u ¿ V ( G ) with v ' ¿ V ( G ' ) if and only if v ' = p ( u ) . If ¿ 2 ( pG ) = ¿ 2 ( G ) for any permutation p of V ( G ) , then G is called a universal ¿ 2 - fixer. In this work we characterize the cycles and paths that are universal ¿ 2 -fixers. |
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