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Maximum eccentric connectivity index for graphs with given diameter

Hauweele, Pierre ; Hertz, Alain ; Mélot, Hadrien ; Ries, Bernard ; Devillez, Gauvain

In: Discrete Applied Mathematics, 2019, vol. 268, p. 102-111

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...