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Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph

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Author Info
Aouchiche, M.
Bell, F.K.
Cvetkovic, D.
Hansen, P.
Rowlinson, P.
Simic, S.K.
Stevanovic, D.
Abstract

We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have been formulated after some experiments with the programming system AutoGraphiX, designed for finding extremal graphs with respect to given properties by the use of variable neighborhood search. The conjectures are related to the maximal value of the irregularity and spectral spread in n-vertex graphs, to a Nordhaus-Gaddum type upper bound for the index, and to the maximal value of the index for graphs with given numbers of vertices and edges. None of the conjectures has been resolved so far. We present partial results and provide some indications that the conjectures are very hard.

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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 191 (2008)
Issue (Month): 3 (December)
Pages: 661-676
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Handle: RePEc:eee:ejores:v:191:y:2008:i:3:p:661-676

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  1. Michael D. König & tefano Battiston & Mauro Napoletano & Frank Schweitzer, 2008. "The efficiency and evolution of R&D Networks," Documents de Travail de l'OFCE 2008-31, Observatoire Francais des Conjonctures Economiques (OFCE). [Downloadable!]
  2. Michael D. König & S. Battiston & M. Napoletano & F. Schweitzer, 2008. "The Efficiency and Evolution of R&D Networks," Economics working paper series 08/95, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
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