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On the Partition Dimension and the Twin Number of a Graph

Author
Hernando, M.; Mora, M.; Pelayo, I. M.
Type of activity
Report
Date
2016-03-05
Repository
http://hdl.handle.net/2117/87267 Open in new window
URL
http://arxiv.org/pdf/1602.08907v3.pdf Open in new window
Abstract
A partition of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of . The partition dimension of G is the minimum cardinality of a locating partition of G . A pair of vertices u;v of a graph G are called twins if they have exactly the same set of neighbors other than u and v . A twin class is a maximal set of pairwise twin vertices. The twin number of a graph G is the maximum cardinality of a tw...
Citation
Hernando, M., Mora, M., Pelayo, I. M. "On the Partition Dimension and the Twin Number of a Graph". 2016.
Keywords
locating partition, locating set, metric dimension, partition dimension, twin number
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications
DCG - Discrete and Combinatorial Geometry