Automated Results and Conjectures on Average Distance in Graphs

  • Mustapha Aouchiche
  • Pierre Hansen
Part of the Trends in Mathematics book series (TM)

Abstract

Using the AutoGraphiX 2 system, a systematic study is made on generation and proof of relations of the form
$$ \underline b _n \leqslant \bar l \oplus i \leqslant \bar b_n $$

where \( \bar l \) denotes the average distance between distinct vertices of a connected graph G, i one of the invariants: diameter, radius, girth, maximum, average and minimum degree, \( \underline b _n \) and \( \bar b_n \) are best possible lower and upper bounds, functions of the order n of G and ⊕ ∈ −, + ×, /. In 24 out of 48 cases simple bounds are obtained and proved by the system. In 21 more cases, the system provides bounds, 16 of which are proved by hand.

Keywords

Graph Invariant AGX Conjecture Average Distance 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Mustapha Aouchiche
    • 1
  • Pierre Hansen
    • 2
  1. 1.GERAD and Département de mathématiques et de génie industrielÉcole Polytechnique de MontréalMontréalCanada
  2. 2.GERAD and Service de l’enseignement des méthodes quantitatives de gestionHEC MontréalMontréalCanada

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