On the Metric Dimension of Infinite Graphs

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dc.creatorCáceres, J.
dc.creatorHernando, C.
dc.creatorMora, M.
dc.creatorPuertas, M. L.
dc.creatorPelayo, I. M.
dc.date2009-04-30
dc.date.accessioned2026-07-07T13:10:33Z
dc.date.available2026-07-07T13:10:33Z
dc.descriptionA set of vertices $S$ \emph{resolves} a graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of a graph $G$ is the minimum cardinality of a resolving set. In this paper we study the metric dimension of infinite graphs such that all its vertices have finite degree. We give necessary conditions for those graphs to have finite metric dimension and characterize infinite trees with finite metric dimension. We also establish some results about the metric dimension of the cartesian product of finite and infinite graphs, and give the metric dimension of the cartesian product of several families of graphs.
dc.description17 pages, 17 figures, 3 tables, 16 references
dc.identifierhttps://arxiv.org/abs/0904.4826
dc.identifierhttp://arxiv.org/abs/0904.4826
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229041
dc.subjectCombinatorics
dc.subject05C12; 05C35
dc.titleOn the Metric Dimension of Infinite Graphs
dc.typetext

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