The threshold strong dimension of a graph

Benakli, Nadia; Bong, Novi H.; (Gosselin), Shonda Dueck; Eroh, Linda; Novick, Beth; Oellermann, Ortrud R.

doi:10.1016/j.disc.2021.112402

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Combinatorial Aspects Of Adim K (G)1

Introduction1

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2021

2022

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Cited by 3 publications

(2 citation statements)

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“…This concept was first presented in [144]. A strong variant (defined in a natural way with respect to the strong metric dimension) of it was published in [22].…”

Section: Combinatorial Aspects Of Adim K (G)mentioning

confidence: 99%

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Kuziak,

Yero

2021

Preprint

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“…This concept was first presented in [144]. A strong variant (defined in a natural way with respect to the strong metric dimension) of it was published in [22].…”

Section: Combinatorial Aspects Of Adim K (G)mentioning

confidence: 99%

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Kuziak,

Yero

2021

Preprint

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“…Mol, Murphy and Oellermann [13] considered the question of how much the metric dimension of a graph can be reduced by adding edges, defining the threshold dimension of a graph G to be the minimum of β(H) over all graphs H on V (G) for which G is a subgraph. The analogous concept for strong dimension is introduced in [3]. Metric dimension of random graphs is studied in [4].…”

Section: Introductionmentioning

confidence: 99%

Metric dimension of growing infinite graphs

Bíró¹,

Novick²,

Olejnikova³

2022

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We investigate how the metric dimension of infinite graphs change when we add edges to the graph. Our two main results: (1) there exists a growing sequence of graphs (under the subgraph relation, but without adding vertices) for which the metric dimension changes between finite and infinite infinitely many times; (2) finite changes in the edge set can not change the metric dimension from finite to infinite or vice versa.

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