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Metric dimension (graph theory)

Known as: Metric dimension 
In graph theory, the metric dimension of a graph G is the minimum cardinality of a subset S of vertices such that all other vertices are uniquely… Expand
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Related topics

Related topics

20 relations
AlgorithmicaApproximation algorithmCographComplex network zeta function
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Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2016
2016
k-Metric Antidimension: a Privacy Measure for Social Graphs
The study and analysis of social graphs impacts on a wide range of applications, such as community decision making support and… Expand
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2015
2015
The structure and metric dimension of the power graph of a finite group
The power graph P G of a finite group G is the graph with the vertex set G , where two distinct vertices are adjacent if one is a… Expand
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2014
2014
Computing the metric dimension of wheel related graphs
Abstract An ordered set W = { w 1 , … , w k } ⊆ V ( G ) of vertices of G is called a resolving set or locating set for G if every… Expand
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2012
2012
The metric dimension of the lexicographic product of graphs
For an ordered set $W=\{w_1,w_2,...,w_k\}$ of vertices and a vertex $v$ in a connected graph $G$, the ordered $k$-vector $r(v|W… Expand
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Highly Cited
2010
Highly Cited
2010
Extremal Graph Theory for Metric Dimension and Diameter
Let Gβ,D be the set of graphs with metric dimension β and diameter D. The first contribution is to characterize the graphs in G… Expand
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2009
2009
On the Metric Dimension of Infinite Graphs
A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vector of distances to the… Expand
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Highly Cited
2007
Highly Cited
2007
On the Metric Dimension of Cartesian Products of Graphs
A set of vertices $S$ resolves a graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in… Expand
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Highly Cited
2006
Highly Cited
2006
Gravity and the standard model with neutrino mixing
ARASON H, 1992, PHYS REV D, V46, P3945, DOI 10.1103-PhysRevD.46.3945; Atiyah M.F., 1967, K THEORY; Avramidi I. G., 1986, THESIS… Expand
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Highly Cited
2000
Highly Cited
2000
Resolvability in graphs and the metric dimension of a graph
Abstract For an ordered subset W={w1,w2,…,wk} of vertices in a connected graph G and a vertex v of G, the metric representation… Expand
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Highly Cited
1996
Highly Cited
1996
Landmarks in Graphs
Navigation can be studied in a graph-structured framework in which the navigating agent (which we shall assume to be a point… Expand
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