Discrepancies between metric dimension and partition dimension of a connected graph

DOI10.1016/j.disc.2007.08.089zbMath1184.05033OpenAlexW2002199085MaRDI QIDQ2519818

Ioan Tomescu

Publication date: 27 January 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2007.08.089

zbMATH Keywords

basiseccentricityinteger latticeresolving setmetric dimensionpartition dimensionchessboard distancecity block distancediametral vertex

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (22)

On the partition dimension of trees ⋮ Partition dimension of projective planes ⋮ A note on the partition dimension of Cartesian product graphs ⋮ The partition dimension of strong product graphs and Cartesian product graphs ⋮ On the strong metric dimension of Cartesian and direct products of graphs ⋮ Partition dimension of certain classes of series parallel graphs ⋮ On the strong partition dimension of graphs ⋮ On the partition dimension of two-component graphs ⋮ On the metric dimension of corona product graphs ⋮ Approximation complexity of metric dimension problem ⋮ A note on \(k\)-metric dimensional graphs ⋮ On the partition dimension of a class of circulant graphs ⋮ On the metric dimension of HDN ⋮ The metric dimension of the lexicographic product of graphs ⋮ On Approximation Complexity of Metric Dimension Problem ⋮ Strong metric dimension of rooted product graphs ⋮ Resolving dominating partitions in graphs ⋮ On some resolving partitions for the lexicographic product of two graphs ⋮ The partition dimension of circulant graphs ⋮ On the Metric Dimension of Infinite Graphs ⋮ A method to construct graphs with certain partition dimension ⋮ Finite metric and 𝑘-metric bases on ultrametric spaces

Cites Work

• On \(k\)-dimensional graphs and their bases
• Resolvability in graphs and the metric dimension of a graph
• The partition dimension of a graph
• Metric bases in digital geometry
• Structure-activity maps for visualizing the graph variables arising in drug design
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