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Maximum Eccentric Connectivity Index for Graphs with Given Diameter
Hauweele, Pierre; Hertz, Alain; Mélot, Hadrien et al.
2019In Discrete Applied Mathematics
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Abstract :
[en] The eccentricity of a vertex v in a graph G is the maximum distance between v and any other vertex of G. The diameter of a graph G is the maximum eccentricity of a vertex in G. The eccentric connectivity index of a connected graph is the sum over all vertices of the product between eccentricity and degree. 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 :
Maximum Eccentric Connectivity Index for Graphs with Given Diameter
Publication date :
15 September 2019
Journal title :
Discrete Applied Mathematics
ISSN :
0166-218X
eISSN :
1872-6771
Publisher :
Elsevier, Amsterdam, Netherlands
Peer reviewed :
Peer Reviewed verified by ORBi
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
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