Computing the Metric Dimension of a Graph from Primary Subgraphs

Dorota Kuziak, Juan A. Rodríguez-Velázquez, and Ismael G. Yero. "Computing the Metric Dimension of a Graph from Primary Subgraphs." Discussiones Mathematicae Graph Theory 37.1 (2017): 273-293. <http://eudml.org/doc/288048>.

@article{DorotaKuziak2017,
abstract = {Let G be a connected graph. Given an ordered set W = \{w1, . . . , wk\} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . . , d(u, wk)), where d(u, wi) denotes the distance between u and wi. The set W is a metric generator for G if every two different vertices of G have distinct representations. A minimum cardinality metric generator is called a metric basis of G and its cardinality is called the metric dimension of G. It is well known that the problem of finding the metric dimension of a graph is NP-hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices. The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.},
author = {Dorota Kuziak, Juan A. Rodríguez-Velázquez, Ismael G. Yero},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {metric dimension; metric basis; primary subgraphs; rooted product graphs; corona product graphs},
language = {eng},
number = {1},
pages = {273-293},
title = {Computing the Metric Dimension of a Graph from Primary Subgraphs},
url = {http://eudml.org/doc/288048},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Dorota Kuziak
AU - Juan A. Rodríguez-Velázquez
AU - Ismael G. Yero
TI - Computing the Metric Dimension of a Graph from Primary Subgraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 1
SP - 273
EP - 293
AB - Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . . , d(u, wk)), where d(u, wi) denotes the distance between u and wi. The set W is a metric generator for G if every two different vertices of G have distinct representations. A minimum cardinality metric generator is called a metric basis of G and its cardinality is called the metric dimension of G. It is well known that the problem of finding the metric dimension of a graph is NP-hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices. The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.
LA - eng
KW - metric dimension; metric basis; primary subgraphs; rooted product graphs; corona product graphs
UR - http://eudml.org/doc/288048
ER -