[en] 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.
Research center :
CREMMI - Modélisation mathématique et informatique
Disciplines :
Electrical & electronics engineering Mathematics
Author, co-author :
Hauweele, Pierre ; Université de Mons > Faculté des Sciences > Systèmes d'information
Hertz, Alain
Mélot, Hadrien ; Université de Mons > Faculté des Sciences > Service Algorithmique
Ries, Bernard
Devillez, Gauvain ; Université de Mons > Faculté des Sciences > Service d'Informatique théorique
Language :
English
Title :
Extremal results on the eccentric connectivity index
Publication date :
14 August 2019
Number of pages :
28
Event name :
Ghent Graph Theory Workshop On Structure and Algorithms
Event place :
Ghent, Belgium
Event date :
2019
Research unit :
S825 - Algorithmique
Research institute :
R300 - Institut de Recherche en Technologies de l'Information et Sciences de l'Informatique R150 - Institut de Recherche sur les Systèmes Complexes
