Aequationes mathematicae

, Volume 82, Issue 1–2, pp 65–79 | Cite as

Rank numbers for some trees and unicyclic graphs

  • Emily Sergel
  • Peter Richter
  • Anh Tran
  • Patrick Curran
  • Jobby Jacob
  • Darren A. Narayan


A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices of the same rank contains a vertex of strictly larger rank. The rank number of a graph is the fewest number of labels that can be used in a ranking. In this paper we determine rank numbers for some trees and unicyclic graphs.


Primary 05C78 Secondary 05C15 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Emily Sergel
    • 1
  • Peter Richter
    • 2
  • Anh Tran
    • 3
  • Patrick Curran
    • 3
  • Jobby Jacob
    • 3
  • Darren A. Narayan
    • 3
  1. 1.Department of MathematicsRutgers UniversityPiscatawayUSA
  2. 2.Department of MathematicsUniversity of RochesterRochesterUSA
  3. 3.School of Mathematical SciencesRochester Institute of TechnologyRochesterUSA

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