New results on metric-locating-dominating sets of graphs
A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number. In this paper, we undertake a study that, in...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2016 |
| 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:2117/96709 |
| Acceso en línea: | https://hdl.handle.net/2117/96709 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Number theory metric-locating-dominating set resolving set dominati ng set locating- dominating set doubly resolving set Grafs, Teoria de Nombres, Teoria dels Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominatin g sets to other special sets: resolving sets, dominating sets, locating-dominating set s and doubly resolving sets. We first characterize classes of trees according to cer tain relationships between their metric-location-domination number and thei r metric dimension and domination number. Then, we show different methods to tran sform metric- locating-dominating sets into locating-dominating sets a nd doubly resolving sets. Our methods produce new bounds on the minimum cardinalities of all those sets, some of them involving parameters that have not been related so far |
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