On the k-partition dimension of graphs
As a generalization of the concept of the partition dimension of a graph, this article introduces the notion of the k-partition dimension. Given a nontrivial connected graph G=(V,E), a partition II of V is said to be a k-partition generator of G if any pair of different vertices u,v E V is distingui...
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| Tipo de documento: | artigo |
| Estado: | Versión enviada para evaluación y publicación |
| Data de publicação: | 2018 |
| País: | España |
| Recursos: | Universitat Oberta de Catalunya (UOC) |
| Repositório: | O2, repositorio institucional de la UOC |
| OAI Identifier: | oai:openaccess.uoc.edu:10609/93187 |
| Acesso em linha: | https://hdl.handle.net/10609/93187 |
| Access Level: | Acceso aberto |
| Palavra-chave: | k-partition dimension k-metric dimension partition dimension metric dimension dimensión k-partición dimensión k-métrica dimensión de partición dimensión métrica dimensió k-partició dimensió k-mètrica dimensió de partició dimensió mètrica Computers Ordinadors Ordenadores |
| Resumo: | As a generalization of the concept of the partition dimension of a graph, this article introduces the notion of the k-partition dimension. Given a nontrivial connected graph G=(V,E), a partition II of V is said to be a k-partition generator of G if any pair of different vertices u,v E V is distinguished by at least k vertex sets of II i.e., there exist at least k vertex sets S1,...,Sk E II such that d(u,Si) /= d(v,Si) for every i E {1,...,k}. A k-partition generator of G with minimum cardinality among all their k-partition generators is called a k-partition basis of G and its cardinality the k-partition dimension of G. A nontrivial connected graph G is k-partition dimensional if k is the largest integer such that G has a k-partition basis. We give a necessary and sufficient condition for a graph to be r-partition dimensional and we obtain several results on the k-partition dimension for k E {1,...,r}. |
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