Characterizing 1-metric antidimensional trees and unicyclic graphs

Trujillo Rasua, Rolando and Yero, Ismael G 2016, Characterizing 1-metric antidimensional trees and unicyclic graphs, Computer journal, vol. 59, no. 8, pp. 1264-1273, doi: 10.1093/comjnl/bxw021.

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Title Characterizing 1-metric antidimensional trees and unicyclic graphs
Author(s) Trujillo Rasua, RolandoORCID iD for Trujillo Rasua, Rolando
Yero, Ismael G
Journal name Computer journal
Volume number 59
Issue number 8
Start page 1264
End page 1273
Total pages 10
Publisher Oxford University Press
Place of publication Oxford, Eng.
Publication date 2016-08-01
ISSN 0010-4620
Keyword(s) k-antiresolving set
k-metric antidimension
social networks
science & technology
hardware & architecture
information systems
software engineering
theory & methods
computer science
Summary Let G=(V,E) be a simple connected graph and S={w1, wt} V an ordered subset of vertices. The metric representation of a vertex u V with respect to S is the t-vector r(u|S)=(dG(u,w1), dG(u,wt)), where dG(u,v) represents the length of a shortest u-v path in G. A set S is a k-antiresolving set if k is the largest positive integer such that for every vertex v V-S there exist other k-1 different vertices v1, vk-1 V-S such that v,v1, vk-1 have the same metric representation with respect to S. The k-metric antidimension of G is the minimum cardinality among all the k-antiresolving sets for G, and G is k-metric antidimensional if k is the largest integer such that G contains a k-antiresolving set. In this article, we provide characterizations for 1-metric antidimensional trees and unicyclic graphs, together with computationally efficient algorithms to decide whether these types of graphs are 1-metric antidimensional.
Language eng
DOI 10.1093/comjnl/bxw021
Field of Research 08 Information And Computing Sciences
HERDC Research category C1.1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2016, The British Computer Society
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