On the partition dimension of trees

Given an ordered partition Π={P1,P2,…,Pt} of the vertex set V of a connected graph G=(V,E), the partition representation of a vertex v∈V with respect to the partition Π is the vector r(v|Π)=(d(v,P1),d(v,P2),…,d(v,Pt)), where d(v,Pi) represents the distance between the vertex v and the set Pi. A part...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 166; pp. 204 - 209
Main Authors Rodriguez-Velazquez, Juan, Yero, Ismael, Lemanska, Magdalena
Format Journal Article
LanguageEnglish
Published Elsevier B.V 31.03.2014
Subjects
Graphs
Mathematical analysis
Partition dimension
Partitions
Representations
Resolving partition
Resolving sets
Trees
Vectors (mathematics)
Resolving sets
Resolving partition
Partition dimension
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Summary:Given an ordered partition Π={P1,P2,…,Pt} of the vertex set V of a connected graph G=(V,E), the partition representation of a vertex v∈V with respect to the partition Π is the vector r(v|Π)=(d(v,P1),d(v,P2),…,d(v,Pt)), where d(v,Pi) represents the distance between the vertex v and the set Pi. A partition Π of V is a resolving partition of G if different vertices of G have different partition representations, i.e., for every pair of vertices u,v∈V, r(u|Π)≠r(v|Π). The partition dimension of G is the minimum number of sets in any resolving partition of G. In this paper we obtain several tight bounds on the partition dimension of trees.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2013.09.026