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http://hdl.handle.net/10609/93187
Title: | On the k-partition dimension of graphs |
Author: | Estrada-Moreno, Alejandro |
Others: | Universitat Oberta de Catalunya (UOC) |
Citation: | Estrada-Moreno, A. (2020). On the k-partition dimension of graphs. Theoretical Computer Science, 806(), 42-52. doi: 10.1016/j.tcs.2018.09.022. |
Abstract: | 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}. |
Keywords: | k-partition dimension k-metric dimension partition dimension metric dimension |
DOI: | 10.1016/j.tcs.2018.09.022 |
Document type: | info:eu-repo/semantics/article |
Version: | info:eu-repo/semantics/submittedVersion |
Issue Date: | 16-Sep-2018 |
Publication license: | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Appears in Collections: | Articles cientÍfics Articles |
Files in This Item:
File | Description | Size | Format | |
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kpartition.pdf | Preprint | 389,71 kB | Adobe PDF | View/Open |
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