Groupe d’études et de recherche en analyse des décisions

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 \(D\leq n-1\), 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 \(n\).

, 14 pages