On the metric dimension, the upper dimension and the resolving number of graphs
This paper deals with three resolving parameters: the metric dimension, the upper dimension and the resolving number. We first answer a question raised by Chartrand and Zhang asking for a characterization of the graphs with equal metric dimension and resolving number. We also solve in the affirmativ...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2013 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/38830 |
| Acesso em linha: | http://hdl.handle.net/11441/38830 https://doi.org/10.1016/j.dam.2013.01.026 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Resolving set Metric dimension Upper dimension Resolving number |
| Resumo: | This paper deals with three resolving parameters: the metric dimension, the upper dimension and the resolving number. We first answer a question raised by Chartrand and Zhang asking for a characterization of the graphs with equal metric dimension and resolving number. We also solve in the affirmative a conjecture posed by Chartrand, Poisson and Zhang about the realization of the metric dimension and the upper dimension. Finally, we prove that no integer a≥4a≥4 is realizable as the resolving number of an infinite family of graphs. |
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