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2019-08-14 - Colloque/Présentation - communication orale - Anglais - 28 page(s)

Hauweele Pierre , Hertz Alain, Mélot Hadrien , Ries Bernard, Devillez Gauvain , "Extremal results on the eccentric connectivity index" in Ghent Graph Theory Workshop On Structure and Algorithms, Ghent, Belgium, 2019

  • Codes CREF : Mathématiques (DI1100), Théorie des graphes (DI1146), Recherche opérationnelle (DI1150), Informatique mathématique (DI1160)
  • Unités de recherche UMONS : Algorithmique (S825)
  • Instituts UMONS : Institut de Recherche en Technologies de l’Information et Sciences de l’Informatique (InforTech), Institut de Recherche sur les Systèmes Complexes (Complexys)
  • Centres UMONS : Modélisation mathématique et informatique (CREMMI)
Texte intégral :

Abstract(s) :

(Anglais) The eccentric connectivity index of a connected graph is the sum over all vertices of the product between eccentricity (maximum distance to any other vertex) and degree. Alternatively, it is the sum, over all edges, of the eccentricities of both their vertices. We will present some known and new extremal results about this invariant. Especially, given two integers n and D with D <= n-1, we characterize those graphs which have the largest eccentric connectivity index among all connected graphs of order n and diameter D. As a corollary, we also characterize those graphs which have the largest eccentric connectivity index among all connected graphs of a given order n.