论文标题
Wiener索引和图形，几乎一半的顶点满足Šoltés属性
Wiener index and graphs, almost half of whose vertices satisfy Šoltés property
论文作者
论文摘要
连接图$ g $的Wiener索引$ w（g）$是所有对$ g $的顶点之间的距离之和。在1991年，šoltés提出了找到所有图表$ g $的问题，以便对于每个顶点$ v $ equation $ w（g）= w（g-v）$保持。周期$ c_ {11} $是该属性唯一已知的图表。在本文中，我们考虑了以下原始问题的放松：找到具有很大比例的顶点的图形，以便删除其中任何一个不会改变图形的Wiener索引。作为主要结果，我们构建了一系列无限的图形，其中此类顶点的比例趋于$ \ frac {1} {2} $。
The Wiener index $W(G)$ of a connected graph $G$ is a sum of distances between all pairs of vertices of $G$. In 1991, Šoltés formulated the problem of finding all graphs $G$ such that for every vertex $v$ the equation $W(G)=W(G-v)$ holds. The cycle $C_{11}$ is the only known graph with this property. In this paper we consider the following relaxation of the original problem: find a graph with a large proportion of vertices such that removing any one of them does not change the Wiener index of a graph. As the main result, we build an infinite series of graphs with the proportion of such vertices tending to $\frac{1}{2}$.
