Proximity in triangulations and quadrangulations

Eva Czabarka, Peter Dankelmann, Trevor Olsen, Laszlo A. Szekely

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Let G be a connected graph. If (Formula Presented) denotes the arithmetic mean of the distances from v to all other vertices of G, then the proximity, (Formula Presented), of G is defined as the smallest value of (Formula Presented) over all vertices v of G. We give upper bounds for the proximity of simple triangulations and quadrangulations of given order and connectivity. We also construct simple triangulations and quadrangulations of given order and connectivity that match the upper bounds asymptotically and are likely optimal.

Original languageEnglish
Pages (from-to)425-446
Number of pages22
JournalElectronic Journal of Graph Theory and Applications
Issue number2
Publication statusPublished - 2022


  • Average distance
  • Connectivity
  • Distance
  • Maximal
  • Planar graph
  • Proximity
  • Quadrangulation
  • Triangulation
  • Upper bounds

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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