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arXiv · 1808.10203

Maximum Eccentric Connectivity Index for Graphs with Given Diameter

Pierre Hauweele·Alain Hertz·Hadrien Mélot·Bernard Ries·Gauvain Devillez
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Abstract

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 $n$.

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Pierre Hauweele, Alain Hertz, Hadrien Mélot, Bernard Ries, Gauvain Devillez. 2018-08-30. Maximum Eccentric Connectivity Index for Graphs with Given Diameter. https://doi.org/10.1016/j.dam.2019.04.031

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