The Local Metric Dimension of the Lexicographic Product of Graphs

The metric dimension is quite a well-studied graph parameter. Recently, the local metric dimension and the adjacency dimension have been introduced and studied. In this paper, we give a general formula for the local metric dimension of the lexicographic product G ∘ H of a connected graph G of order...

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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 42; no. 5; pp. 2481 - 2496
Main Authors Barragán-Ramírez, Gabriel A., Estrada-Moreno, Alejandro, Ramírez-Cruz, Yunior, Rodríguez-Velázquez, Juan A.
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 15.09.2019
Springer Nature B.V
Subjects
Applications of Mathematics
Graphs
Mathematics
Mathematics and Statistics
05C76
05C12
Lexicographic product graphs
Local adjacency dimension
Local metric dimension
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Summary:The metric dimension is quite a well-studied graph parameter. Recently, the local metric dimension and the adjacency dimension have been introduced and studied. In this paper, we give a general formula for the local metric dimension of the lexicographic product G ∘ H of a connected graph G of order n and a family H composed of n graphs. We show that the local metric dimension of G ∘ H can be expressed in terms of the numbers of vertices in the true twin equivalence classes of G , and the local adjacency dimension of the graphs in H .
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-018-0611-3