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二部图的距离k次方和问题
引用本文:耿显亚,赵红锦,徐李立.二部图的距离k次方和问题[J].数学杂志,2017,37(6):1111-1117.
作者姓名:耿显亚  赵红锦  徐李立
作者单位:安徽理工大学数学与大数据学院, 安徽 淮南 232001,安徽理工大学数学与大数据学院, 安徽 淮南 232001,华中师范大学数学与统计学院, 湖北 武汉 430079
基金项目:Supported by National Natural Science Foundation of China (11401008; 61672001; 61572035; 61402011) and China Postdoctoral Science Foundation (2016M592030).
摘    要:本文定义SkG)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dn顶点连通二部图SkG)的下界,并确定了达到下界所对应的的极图.

关 键 词:二部图  直径  极图
收稿时间:2017/1/8 0:00:00
修稿时间:2017/4/1 0:00:00

ON THE SUM OF k-POWER OF ALL DISTANCES IN BIPARTITE GRAPHS
GENG Xian-y,ZHAO Hong-jin and XU Li-li.ON THE SUM OF k-POWER OF ALL DISTANCES IN BIPARTITE GRAPHS[J].Journal of Mathematics,2017,37(6):1111-1117.
Authors:GENG Xian-y  ZHAO Hong-jin and XU Li-li
Institution:School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, China,School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, China and School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
Abstract: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.
Keywords:bipartite graph  diameter  extremal graph
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