论文标题
给定直径的双环图的最小谐波指数
The minimum harmonic index for bicyclic graphs with given diameter
论文作者
论文摘要
图$ g $的谐波索引定义为所有边缘$ uv $ of $ g $的权重$ \ frac {2} {d（u）+d（v）} $，其中$ d（u）$是$ g $ in $ g $的顶点$ u $的程度。在本文中，我们找到了订单$ n $和直径$ d $的BICICLIC图的最小谐波指数。我们还表征了达到最小结合的所有双环图。
The harmonic index of a graph $G$, is defined as the sum of weights $\frac{2}{d(u)+d(v)}$ of all edges $uv$ of $G$, where $d(u)$ is the degree of the vertex $u$ in $G$. In this paper we find the minimum harmonic index of bicyclic graph of order $n$ and diameter $d$. We also characterized all bicyclic graphs reaching the minimum bound.
