dc.contributor.author Currie, James dc.contributor.author Oellerman, Ortrud R. dc.date.accessioned 2019-11-20T19:48:48Z dc.date.available 2019-11-20T19:48:48Z dc.date.issued 2001 dc.identifier.citation Currie, James, and Ortrud R. Oellerman, "The metric dimension and metric independence of a graph," Journal of Combinatorial Mathematics and Combinatorial Computing 39 (2001): 157–167. en_US dc.identifier.uri http://hdl.handle.net/10680/1746 dc.description.abstract A vertex x of a graph G resolves two vertices u and v of G if the en_US distance from x to u does not equal the distance from x to v. A set S of vertices of G is a resolving set for G if every two distinct vertices of G are resolved by some vertex of S. The minimum cardinality of a resolving set for G is called the metric dimension of G. The problem of nding the metric dimension of a graph is formulated as an integer pro- gramming problem. It is shown how a relaxation of this problem leads to a linear programming problem and hence to a fractional version of the metric dimension of a graph. The linear programming dual of this problem is considered and the solution to the corresponding integer programming problem is called the metric independence of the graph. It is shown that the problem of deciding whether, for a given graph G, the metric dimension of G equals its metric independence is NP- complete. Trees with equal metric dimension and metric independence are characterized. The metric independence number is established for various classes of graphs. dc.language.iso en en_US dc.publisher The Charles Babbage Research Centre en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.subject graphs, metric dimension, metric independence en_US dc.title The metric dimension and metric independence of a graph en_US dc.type Article en_US dc.description.version Preprint
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