中文摘要：

一个连通图的维纳指标定义为它的所有不同顶点对之间距离的和.给出图的两个变换以及计算这两个变换下新图维纳指标的公式,借助这两个变换刻划所有给定度序列的毛毛虫图中具有最小维纳指标的图.

英文摘要：

Wiener index of a connected graph is the sum of distances among all pairs of vertices in the graph. Two graphictransformations and the formulas for obtaining Wiener index of new graphs were given. With these transformations, the treeshaving the smallest Wiener index among all caterpillars with a given degree sequence were characterized.