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…

Papers overview

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2019

Let G be a simple graph. A set of vertices, called V (G) and a set of edges, called E(G) are two sets which form graph G. W is a…

2018

The concept of metric dimension was proposed to model robot navigation where the places of navigating agents can change among…

2017

2015

A distance between two vertices of a connected graph is the shortest distance between them. The metric dimension of a connected…

2013

2011

For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W ) := (d…

2010

A subset of vertices S resolves a graph G if every vertex of G is uniquely determined by its vector of distances to the vertices…

2001

For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the (metric) representation of v…

1993

For every integer m, k, and n such that 0 ≤ m ≤ n − 1 and m ≤ k ≤ min{2m, n − 1}, we construct a subspace S m,k n = in Euclidean…

1982