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Erratum to “On the strong metric dimension of the strong products of graphs”

100%

Kuziak D., Yero I. G., Rodríguez-Velázquez J. A.

Open Mathematics

2015

tom 13

nr 1

The original version of the article was published in Open Mathematics (formerly Central European Journal of Mathematics) 13 (2015) 64–74. Unfortunately, the original version of this article contains a mistake: in Lemma 2.17 appears that for any C1-graph G and any graph H, β (G ⊠ H) ≤ β (G)(β(H)+1), while should be β (G ⊠ H) ≤ β(H) (β(G)+1). In this erratum we correct the lemma, its proof and some of its consequences.

On the strong metric dimension of the strong products of graphs

100%

Kuziak D., Yero I. G., Rodríguez-Velázquez J. A.

Open Mathematics

2015

tom 13

nr 1

Let G be a connected graph. A vertex w ∈ V.G/ strongly resolves two vertices u,v ∈ V.G/ if there exists some shortest u-w path containing v or some shortest v-w path containing u. A set S of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong resolving set for G is called the strong metric dimension of G. It is well known that the problem of computing this invariant is NP-hard. In this paper we study the problem of finding exact values or sharp bounds for the strong metric dimension of strong product graphs and express these in terms of invariants of the factor graphs.

Ograniczanie wyników

2 Open Mathematics

2 Kuziak D.

2 Rodríguez-Velázquez J. A.

2 Yero I. G.

2 2015

Wyniki wyszukiwania

Erratum to “On the strong metric dimension of the strong products of graphs”

On the strong metric dimension of the strong products of graphs