无圈共轭分子图的调和指标

he harmonic index $H(G)$ of a graph $G$ is defined as the sum ofweights $ rac{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 paper, we firstpresent a sharp lower bound on the harmonic index of acyclicconjugated molecular graphs (trees with a perfect matching). A sharplower bound on the harmonic index of acyclic graphs is also given interms of the order and given size of matching.