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

Mustapha Aouchiche; Pierre Hansen; Maolin Zheng

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

Mustapha Aouchiche
, Pierre Hansen
, Maolin Zheng

Research output: Contribution to journal › Article › peer-review

Abstract

Using the AutoGraphiX 2 system (AGX2), we study relations between graph invariants of the form lb_n ≤ R ⊕ i ≤ ub_n 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 lb_n and ub_n 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 language	English
Pages (from-to)	541-550
Number of pages	10
Journal	Match
Volume	56
Issue number	3
Publication status	Published - 2006
Externally published	Yes

ASJC Scopus subject areas

General Chemistry
Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

Cite this

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author = "Mustapha Aouchiche and Pierre Hansen and Maolin Zheng",

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AB - 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.

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

Abstract

ASJC Scopus subject areas

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