The geometric–arithmetic index and the chromatic number of connected graphs

Mustapha Aouchiche, Pierre Hansen

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In the present paper, we compare the geometric–arithmetic index GA and the chromatic number χ of a connected graph with given order. We prove, among other results, an upper bound on the ratio GA∕χ. We also prove lower bounds on the chromatic number in terms of geometric–arithmetic index and number of vertices of a connected graph. The results obtained for the chromatic number χ are extended to the clique number ω.

Original languageEnglish
Pages (from-to)207-212
Number of pages6
JournalDiscrete Applied Mathematics
Publication statusPublished - Dec 11 2017
Externally publishedYes


  • Chromatic number
  • Clique number
  • Conjecture
  • Geometric–arithmetic index
  • Graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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