论文标题
带有给定数量均衡顶点的Unicycle图的Wiener索引
Wiener index of unicycle graphs with given number of even degree vertices
论文作者
论文摘要
连接图的Wiener索引是所有不同顶点对的距离的总和。维纳（Wiener）在1947年引入了它，以通过拟合烷烃化合物的几种特性的实验数据来分析分支的某些方面。用$ \ Mathcal {u} _ {n，r} $用$ n $顶点和$ r $ Vertices均匀度。在本文中，我们在$ \ mathcal {u} _ {n，r} $中以最小维也纳索引中的图表呈现一个结构性结果，当$ r \ leq \ frac \ frac {n+3} {2} $时完全表征了此类图。
The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane compounds. Denote by $\mathcal{U}_{n,r}$ the set of unicyclic graphs with $n$ vertices and $r$ vertices of even degree. In this paper we present a structural result on the graphs in $\mathcal{U}_{n,r}$ with minimum Wiener index and completely characterize such graphs when $ r\leq \frac{n+3}{2}$.
