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Graphs and Combinatorics

, Volume 35, Issue 3, pp 599–609 | Cite as

Bounds on the Identifying Codes in Trees

  • Hadi Rahbani
  • Nader Jafari RadEmail author
  • Seyed Masoud MirRezaei
Original Paper
  • 38 Downloads

Abstract

In this paper, we continue the study of identifying codes in graphs, introduced by Karpovsky et al. (IEEE Trans Inf Theory 44:599–611, 1998). A subset S of vertices in a graph G is an identifying code if for every pair of vertices x and y of G, the sets \(N[x]\cap S\) and \(N[y]\cap S\) are non-empty and different. The minimum cardinality of an identifying code in G is denoted by M(G). We show that for a tree T with \(n\ge 3\) vertices, \(\ell \) leaves and s support vertices, \((2n-s+3)/4\le M(T) \le (3n+2\ell -1)/5\). Moreover, we characterize all trees achieving equality for these bounds.

Keywords

Identifying code Tree 

Mathematics Subject Classification

05C69 

Notes

Acknowledgements

The authors would like to thank both referees for their careful review and many helpful comments.

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  • Hadi Rahbani
    • 1
  • Nader Jafari Rad
    • 2
    Email author
  • Seyed Masoud MirRezaei
    • 3
  1. 1.Department of MathematicsShahrood University of TechnologyShahroodIran
  2. 2.Department of MathematicsShahed UniversityTehranIran
  3. 3.Department of Electrical EngineeringShahrood University of TechnologyShahroodIran

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