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Discrete Mathematics Letters
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Article . 2023
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Article . 2023
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Claim

The Edge Partition Dimension of Graphs

The edge partition dimension of graphs
descriptionPublicationkeyboard_double_arrow_right Article 30 Mar 2023 Spain English Publisher:Shahin Digital PublisherJournal:Discrete Mathematics Letters, volume 12, pages 34-39 (eissn: 2664-2557, Copyright policy )
Authors: Kuziak, Dorota; Maritz, Elizabeth; Vetrìk, Tomas; González Yero, Ismael;

doi: 10.47443/dml.2023.010

handle: 10498/32226

The Edge Partition Dimension of Graphs

Abstract

Theedgemetric dimension wasintroduced in 2018 and since then, it has been extensively studied. In this paper, we present a different way to obtain resolving structures in graphs in order to gain more insight into the study of edge resolving sets andresolving partitions. We define the edge partition dimension of a connected graph and bound it for graphs of given order andfor graphswithgivenmaximumdegree. Weobtainexactvaluesoftheedgepartitiondimensionformultipartite graphs. Some relations between the edge partition dimension and partition dimension/edge metric dimension are also presented. Moreover, several open problems for further research are stated.

Country
Spain
Related Organizations
Keywords

edge resolving partition, Distance in graphs, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), edge partition dimension, QA1-939, partition dimension, edge metric dimension, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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gold