Extremal Graph Theory for Metric Dimension and Diameter

C. Hernando, M. Mora, I. M. Pelayo, C. Seara, D. R. Wood

Research output: Contribution to journalArticleResearchpeer-review

22 Citations (Scopus)

Abstract

Let G β, D be the set of graphs with metric dimension β and diameter D. The first contribution is to characterize the graphs in G β, D with order β + D for all values of β and D. The second contribution is to determine the maximum order of a graph in G β, D for all values of D and β. Only a weak upper bound was previously known.

Original languageEnglish
Pages (from-to)339-343
Number of pages5
JournalElectronic Notes in Discrete Mathematics
Volume29
Issue numberSPEC. ISS.
DOIs
Publication statusPublished - 15 Aug 2007
Externally publishedYes

Keywords

  • diameter
  • Graph
  • metric basis
  • metric dimension
  • order
  • resolving set

Cite this