Metric dimension of lexicographic product of some known graphs

For an ordered set W = {w1,w2,...,wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W) := (d(v,w1),d(v,w2),...,d(v,wk)) is called the (metric) representation of v with respect to W, where d(x,y) is the distance between the vertices x and y. The set W is called a resolvi...

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Bibliographic Details
Main Author Jannesari, Mohsen
Format Journal Article
LanguageEnglish
Published 01.02.2022
Subjects
Mathematics - Combinatorics
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Summary:For an ordered set W = {w1,w2,...,wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W) := (d(v,w1),d(v,w2),...,d(v,wk)) is called the (metric) representation of v with respect to W, where d(x,y) is the distance between the vertices x and y. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension. In this paper, we investigate the metric dimension of the lexicographic product of graphs G and H, G[H] for some known graphs.
DOI:10.48550/arxiv.2202.00716