Annals of Operations Research

, Volume 188, Issue 1, pp 415–427 | Cite as

Using size for bounding expressions of graph invariants

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Abstract

With the help of the AutoGraphiX system, we study relations of the form
$$\underline{b}_m \le i_1(G) \oplus i_2(G) \le\overline{b}_m$$
where i 1(G) and i 2(G) are invariants of the graph G, ⊕ is one of the operations −,+,/,×, \(\underline{b}_{m}\) and \(\overline{b}_{m}\) are best possible lower and upper bounding functions depending only one the size m of G. Specifically, we consider pairs of indices where i 1(G) is a measure of distance, i.e., diameter, radius or average eccentricity, and i 2(G) is a measure of connectivity, i.e., minimum degree, edge connectivity and vertex connectivity. Conjectures are obtained and then proved in almost all cases.

Keywords

Size Connectivity Distance Extremal graph AGX 

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References

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Jelena Sedlar
    • 1
  • Damir Vukičević
    • 1
  • Pierre Hansen
    • 2
  1. 1.Department of MathematicsUniversity of SplitSplitCroatia
  2. 2.GERAD and Department of Management SciencesHEC MontréalMontréalCanada

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