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On the metric dimension, the upper dimension and the resolving number of graphs

 

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Author: Garijo Royo, Delia
González Herrera, Antonio
Márquez Pérez, Alberto
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2013
Published in: Discrete Applied Mathematics, 161 (10-11), 1440-1447.
Document type: Article
Abstract: 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.
Size: 367.8Kb
Format: PDF

URI: http://hdl.handle.net/11441/38830

DOI: http://dx.doi.org/10.1016/j.dam.2013.01.026

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