Determining sets, resolving sets, and the exchange property

DOI10.1007/s00373-010-0880-6zbMath1205.05103arXiv0808.1427OpenAlexW2034385267MaRDI QIDQ968219

Debra L. Boutin

Publication date: 5 May 2010

Published in: Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.1427

zbMATH Keywords

exchange propertyresolving setsdetermining sets

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (16)

Is it possible to determine a point lying in a simplex if we know the distances from the vertices? ⋮ On the metric basis in wheels with consecutive missing spokes ⋮ On metric orbit spaces and metric dimension ⋮ Minimum partition of an \(r\)-independence system ⋮ The metric dimension of metric spaces ⋮ On redundant locating-dominating sets ⋮ On the metric dimension and diameter of circulant graphs with three jumps ⋮ On resolvability of a graph associated to a finite vector space ⋮ The metric dimension of geometric spaces ⋮ The full automorphism groups, determining sets and resolving sets of coprime graphs ⋮ On the metric dimension of certain metric manifolds ⋮ Exchange property for resolving sets in power graphs ⋮ THE METRIC DIMENSION OF METRIC MANIFOLDS ⋮ Elimination properties for minimal dominating sets of graphs ⋮ Power graphs and exchange property for resolving sets ⋮ On maximal det-independent (res-independent) sets in graphs

Cites Work

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• On the Metric Dimension of Cartesian Products of Graphs
• The determining number of a Cartesian product
• On the Complexity of Canonical Labeling of Strongly Regular Graphs
• Linear Time Automorphism Algorithms for Trees, Interval Graphs, and Planar Graphs

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