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

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


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.


Graph Theory Connected Graph Variable Neighborhood Search Laplacian Matrix Extremal Graph 
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© 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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