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G-2018-66

Maximum eccentric connectivity index for graphs with given diameter

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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 Dn1, 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.

, 14 pages

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Discrete Applied Mathematics, 268, 102–111, 2019 référence BibTeX