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Extremal graph theory for metric dimension and diameter

Author
Hernando, M.; Mora, M.; Pelayo, I. M.; Seara, C.; Wood, D.
Type of activity
Journal article
Journal
Electronic journal of combinatorics
Date of publication
2010
Volume
17
Number
1 R30
First page
1
Last page
28
Repository
http://hdl.handle.net/2117/8261 Open in new window
URL
http://www.combinatorics.org/ Open in new window
Abstract
A set of vertices S resolves a connected 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 G ,D be the set of graphs with metric dimension and diameter D. It is well-known that the minimum order of a graph in G ,D is exactly + D. The first contribution of this paper is to characterise the graphs in G ,D with order + D for all values of and D. Such a characterisa...
Citation
Hernando, M. [et al.]. Extremal graph theory for metric dimension and diameter. "Electronic journal of combinatorics", 22 Febrer 2010, vol. 17, núm. R30, p. 1-28.
Group of research
CGA -Computational Geometry and Applications
COMBGRAPH - Combinatorics, Graph Theory and Applications
DCG - Discrete and Combinatorial Geometry

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