二部图的距离k次方和问题
ON THE SUM OF k-POWER OF ALL DISTANCES IN BIPARTITE GRAPHS

本文定义Sk（G）为G中所有点对之间距离的k次方之和.利用顶点划分的方法得到了直径为d的n顶点连通二部图Sk（G）的下界，并确定了达到下界所对应的的极图.
Denote the sum of k-power of all distances between all pairs of vertices in G by Sk(G). In this paper, by applying the vertex partition method, sharp bound of all connected n-vertex bipartite graphs of diameter d on the Sk(G) is obtained, and the extremal graphs with the minimal Sk(G) are also characterized