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Variable Neighborhood Search for Extremal Graphs. XI. Bounds on Algebraic Connectivity

  • Slim Belhaiza
  • Nair Maria Maia de Abreu
  • Pierre Hansen
  • Carla Silva Oliveira

Abstract

The algebraic connectivity a(G) of a graph G = (V, E) is the second smallest eigenvalue of its Laplacian matrix. Using the AutoGraphiX (AGX) system, extremal graphs for algebraic connectivity of G in function of its order n = |V| and size m = |E| are studied. Several conjectures on the structure of those graphs, and implied bounds on the algebraic connectivity, are obtained. Some of them are proved, e.g., if GK n
$$a\left( G \right) \leqslant \left\lfloor { - 1 + \sqrt {1 + 2m} } \right\rfloor $$
which is sharp for all m ≥ 2.

Keywords

Graph Theory Connected Graph Variable Neighborhood Search Laplacian Matrix Extremal Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Slim Belhaiza
  • Nair Maria Maia de Abreu
  • Pierre Hansen
  • Carla Silva Oliveira

There are no affiliations available

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