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350
Metric Dimension and Exchange Property for Resolving Sets in RotationallySymmetric Graphs
, 2014
"... Abstract: Metric dimension or location number is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let F be a family of connected graphs Gn: F = (Gn)n≥1 depending on n as follows: the order V(G)  = ϕ(n) and lim n→ ∞ ϕ(n)=∞. If there exists a consta ..."
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Abstract: Metric dimension or location number is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let F be a family of connected graphs Gn: F = (Gn)n≥1 depending on n as follows: the order V(G)  = ϕ(n) and lim n→ ∞ ϕ(n)=∞. If there exists a
The geometry of graphs and some of its algorithmic applications
 COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
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Cited by 524 (19 self)
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that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that distances between vertices in G closely match the distances between
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 S. The metric dimension of G is the minimum cardinality of a resolving set of G. Using bounds on the order of the so called doubly resolving sets, we establish bounds on G�H ..."
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Cited by 70 (5 self)
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A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Using bounds on the order of the so called doubly resolving sets, we establish bounds on G
On the metric dimension of Grassmann graphs
 Discrete Math. Theor. Comput. Sci
"... The metric dimension of a graph Γ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph Gq(n,k) (whose vertices are the ksubspaces of F n q, and are adjacent if they ..."
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Cited by 15 (3 self)
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The metric dimension of a graph Γ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph Gq(n,k) (whose vertices are the ksubspaces of F n q, and are adjacent
On the Metric Dimension of Infinite Graphs
, 2009
"... A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of a graph G is the minimum cardinality of a resolving set. In this paper we study the metric dimension of infinite graphs such that all its vertices ha ..."
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Cited by 1 (0 self)
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A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of a graph G is the minimum cardinality of a resolving set. In this paper we study the metric dimension of infinite graphs such that all its vertices
Metric dimension for random graphs
"... The metric dimension of a graph G is the minimum number of vertices in a subset S of the vertex set of G such that all other vertices are uniquely determined by their distances to the vertices in S. In this paper we investigate the metric dimension of the random graph G(n, p) for a wide range of pro ..."
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Cited by 2 (1 self)
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The metric dimension of a graph G is the minimum number of vertices in a subset S of the vertex set of G such that all other vertices are uniquely determined by their distances to the vertices in S. In this paper we investigate the metric dimension of the random graph G(n, p) for a wide range
RATIONAL METRIC DIMENSION OF GRAPHS
, 2014
"... Copyright c ⃝ 2014 Raghavendra, Sooryanarayana and Hegde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract. Let G = (V;E) be ..."
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;v ∈V −S. The minimum cardinality of a rational resolving set S is called rational metric dimension and denoted by rmd(G). A rational resolving set S with minimum cardinality is called rational metric basis. In this paper, we compute rational metric dimension of standard graphs and hence show
Metric Dimension of Amalgamation of Graphs
, 2013
"... A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let {G1, G2,..., Gn} be a finite collection of graphs and each Gi has a fixed vertex v0i or a ..."
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A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let {G1, G2,..., Gn} be a finite collection of graphs and each Gi has a fixed vertex v0i or a
Results 1  10
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350