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http://hdl.handle.net/2117/8261
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| Citació: | Hernando, M. [et al.]. Extremal graph theory for metric dimension and diameter. "Electronic journal of combinatorics", 22 Febrer 2010, vol. 17, núm. R30, p. 1-28. |
| Títol: | Extremal graph theory for metric dimension and diameter |
| Autor: | Hernando Martín, María del Carmen  ; Mora Giné, Mercè ; Seara Ojea, Carlos ; Wood, David |
| Data: | 22-feb-2010 |
| Tipus de document: | Article |
| Resum: | 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. |
| ISSN: | 1077-8926 |
| URI: | http://hdl.handle.net/2117/8261 |
| Versió de l'editor: | http://www.combinatorics.org/Volume_17/PDF/v17i1r30.pdf |
| Apareix a les col·leccions: | Altres. Enviament des de DRAC
Departaments de Matemàtica Aplicada. Articles de revista
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