Wiener index, defined as the sum of distances between all unordered pairs of vertices, is one of the most popular molecular descriptors. It is well known that among 2-vertex connected graphs on $n\ge 3$ vertices, the cycle $C_n$ attains the maximum value of Wiener index. We show that the second maximum graph is obtained from $C_n$ by introducing a new edge that connects two vertices at distance two on the cycle if $n\ne 6$. If $n\ge 11$, the third maximum graph is obtained from a $4$-cycle by connecting opposite vertices by a path of length $n-3$. We completely describe also the situation for $n\le 10$.

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在双顶点连通图上具有第二和第三最大维纳指数的图

维纳指数，定义为所有无序顶点对之间距离的总和，是最流行的分子描述符之一。众所周知，在$n\ge 3$ 个顶点上的2-顶点连通图中，环$C_n$ 达到Wiener 指数的最大值。我们展示了第二个最大图是通过引入一条新边从 $C_n$ 获得的，该边在 $n\ne 6$ 的情况下连接循环上距离为 2 的两个顶点。如果$n\ge 11$，则通过长度为$n-3$的路径连接相对顶点，从$4$-循环中获得第三个最大图。我们还完整地描述了 $n\le 10$ 的情况。