连通图的Kirchhoff指数排序
Ordering connected graphs by their Kirchhoff indices
摘要：
图$G$的Kirchhoff指数$Kf(G)$是图中所有无序顶点对之间的电阻距离之和，它是由Klein和Randić引入的。本文刻画了具有$p\leq\lfloor\frac{n}{2}\rfloor$的完全图$K_n$中删除$p$边所得到的图中具有Kirchhoff指标的所有极图，并得到了这类图的Kirchhoff指标的一个精确的上界.另外，在所有$n>27$阶的连通图中，完全确定了所有具有第一到第九个最大Kirchhoff指数的图.
英文摘要：
The Kirchhoff index $Kf(G)$ of a graph $G$ is the sum of resistance distances between all unordered pairs of vertices, which was introduced by Klein and Randić. In this paper we characterized all extremal graphs with Kirchhoff index among all graphs obtained by deleting $p$ edges from a complete graph $K_n$ with $p\leq\lfloor\frac{n}{2}\rfloor$ and obtained a sharp upper bound on the Kirchhoff index of these graphs. In addition, all the graphs with the first to ninth maximal Kirchhoff indices are completely determined among all connected graphs of order $n>27$.
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