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Rank numbers for some trees and unicyclic graphs

Abstract

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.

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Correspondence to Darren A. Narayan.

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Sergel, E., Richter, P., Tran, A. et al. Rank numbers for some trees and unicyclic graphs. Aequat. Math. 82, 65–79 (2011). https://doi.org/10.1007/s00010-011-0079-9

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Keywords

  • Primary 05C78
  • Secondary 05C15