Variable neighborhood search for extremal graphs. 18. Conjectures and results about the randić index

Mustapha Aouchiche, Pierre Hansen, Maolin Zheng

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

Using the AutoGraphiX 2 system (AGX2), we study relations between graph invariants of the form lbn ≤ R ⊕ i ≤ ubn where R denotes the Randić index of a graph G = (V, E), i another invariant among matching number μ and the index (or the maximum eigenvalue) λ1, ⊕ denotes one of the four operations +, -, x, /, while lbn and ubn lower and upper bounding functions of the order n of the graph considered which are tight for all n (except possibly very small values due to border effects). Conjectures are obtained in 14 out of 16 cases, 6 of which are proved automatically, 7 are proved by hand and one remains open.

Original languageEnglish
Pages (from-to)541-550
Number of pages10
JournalMatch
Volume56
Issue number3
Publication statusPublished - 2006
Externally publishedYes

ASJC Scopus subject areas

  • Chemistry(all)
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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