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Abstract
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 vv 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.
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Authors (3)
-
Juan Alberto Rodriguez-Velazguez
- University of Tarragona Departament d'Enginyeria Informàtica i Matemàtiques
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Ismael Gonzalez Yero
- University of Cadiz DEPARTAMENTO DE MATEMATICAS ESCUELA POLITECNICA SUPERIOR DE ALGECIRAS
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.dam.2013.09.026
- License
- Copyright (2013 Elsevier B.V)
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
DISCRETE APPLIED MATHEMATICS
no. 166,
pages 204 - 209,
ISSN: 0166-218X - Language:
- English
- Publication year:
- 2014
- Bibliographic description:
- Rodriguez-Velazguez J., Yero I., Lemańska M.: On the partition dimension of trees// DISCRETE APPLIED MATHEMATICS. -Vol. 166, (2014), s.204-209
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.dam.2013.09.026
- Verified by:
- Gdańsk University of Technology
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