关于边修正Szeged指数的极值仙人掌
On extremal cacti with respect to the edge revised Szeged index
摘要：
设$G$是一个连通图. $G$的边缘修正Szeged指数被定义为$Sz^{\ast}_{e}(G)=\sum\limits_{e=uv\in E(G)}(m_{u}(e|G)+\frac{m_{0}(e|G)}{2})(m_{v}(e|G)+\frac{m_{0}(e|G)}{2})$，其中$m_{u}(e|G)$（分别，$m_{v}(e|G)$）是其到顶点的距离为$u$的边的数目（分别地，$v$）小于到顶点的距离$v$（分别地，$u$是与$e$两端等距的边的数目。本文给出了具有阶$n$和$k$圈的仙人掌的最小和次小边修正Szeged指数，并给出了所有达到最小和次小边修正Szeged指数的图.
英文摘要：
Let $G$ be a connected graph. The edge revised Szeged index of $G$ is defined as $Sz^{\ast}_{e}(G)=\sum\limits_{e=uv\in E(G)}(m_{u}(e|G)+\frac{m_{0}(e|G)}{2})(m_{v}(e|G)+\frac{m_{0}(e|G)}{2})$, where $m_{u}(e|G)$ (resp., $m_{v}(e|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$), and $m_{0}(e|G)$ is the number of edges equidistant from both ends of $e$. In this paper, we give the minimal and the second minimal edge revised Szeged index of cacti with order $n$ and $k$ cycles, and all the graphs that achieve the minimal and second minimal edge revised Szeged index are identified.
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