Extremal graph theory for metric dimension and diameter
A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let G ,D be the set of graphs with metric dimension and diameter D. It is well-known...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2010 |
| 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:2117/8261 |
| Acceso en línea: | https://hdl.handle.net/2117/8261 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory order graph distance resolving set metric dimension metric basis diameter Grafs, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let G ,D be the set of graphs with metric dimension and diameter D. It is well-known that the minimum order of a graph in G ,D is exactly + D. The first contribution of this paper is to characterise the graphs in G ,D with order + D for all values of and D. Such a characterisation was previously only known for D 6 2 or 6 1. The second contribution is to determine the maximum order of a graph in G ,D for all values of D and . Only a weak upper bound was previously known. |
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