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

M. Aouchiche, F. K. Bell, D. Cvetković, P. Hansen, P. Rowlinson, S. K. Simić, D. Stevanović

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)661-676
Number of pages16
JournalEuropean Journal of Operational Research
Volume191
Issue number3
DOIs
Publication statusPublished - Dec 16 2008
Externally publishedYes

Keywords

  • Adjacency matrix
  • AutoGraphiX
  • Conjectures
  • Extremal graph
  • Graph
  • Index
  • Irregularity
  • Largest eigenvalue
  • Spectral spread
  • Variable neighborhood search

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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