Diameter and inverse degree

Peter Dankelmann, Henda C. Swart, Paul van den Berg

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


The inverse degree r (G) of a finite graph G = (V, E) is defined as r (G) = ∑v ∈ V frac(1, deg v). We prove that, if G is connected and of order n, then the diameter of G is less than (3 r (G) + 2 + o (1)) frac(log n, log log n). This improves a bound given by Erdös et al. by a factor of approximately 2.

Original languageEnglish
Pages (from-to)670-673
Number of pages4
JournalDiscrete Mathematics
Issue number5-6
Publication statusPublished - 28 Mar 2008
Externally publishedYes


  • Diameter
  • Distance
  • Inverse degree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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