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On the metric dimension of locally finite graphs
by
Ignacio M Pelayo
Universitat Politècnica de Catalunya
Coauthors: Jose Cáceres, Carmen Hernando, Mercè Mora, Maria L. Puertas
A set of vertices S resolves a graph G if every vertex of V(G) is uniquely determined by its vector of distances to the vertices in S. The metric dimension of a graph G is the minimum cardinality of a resolving set. We study the metric dimension of infinite graphs such that all vertices have finite degree. We provide 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 locally finite graphs.
Date received: April 11, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cauz-14.