### A lower bound for the harmonic index of a graph with minimum degree at least three

#### Abstract

The harmonic index $H(G)$ of a graph $G$ is the sum of the weights

$\frac{2}{d(u)+d(v)}$ of all edges $uv$ of $G$, where $d(u)$ denotes

the degree of a vertex $u$ in $G$. In this work, a lower bound for

the harmonic index of a graph with minimum degree at least three is

obtained and the corresponding extremal graph is characterized.

$\frac{2}{d(u)+d(v)}$ of all edges $uv$ of $G$, where $d(u)$ denotes

the degree of a vertex $u$ in $G$. In this work, a lower bound for

the harmonic index of a graph with minimum degree at least three is

obtained and the corresponding extremal graph is characterized.

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