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

In: Graph Theory and Combinatorial Optimization

Author

Listed:
  • Slim Belhaiza
  • Nair Maria Maia 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 G ≠ K n $$a\left( G \right) \leqslant \left\lfloor { - 1 + \sqrt {1 + 2m} } \right\rfloor $$ which is sharp for all m ≥ 2.

Suggested Citation

  • Slim Belhaiza & Nair Maria Maia Abreu & Pierre Hansen & Carla Silva Oliveira, 2005. "Variable Neighborhood Search for Extremal Graphs. XI. Bounds on Algebraic Connectivity," Springer Books, in: David Avis & Alain Hertz & Odile Marcotte (ed.), Graph Theory and Combinatorial Optimization, chapter 0, pages 1-16, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25592-7_1
    DOI: 10.1007/0-387-25592-3_1
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    Cited by:

    1. Yousaf, Shamaila & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2022. "On total irregularity index of trees with given number of segments or branching vertices," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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