| 摘要: |
| 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. |
| 关键词: 二部图 直径 极图 |
| DOI： |
| 分类号:O157.6 |
| 基金项目:Supported by National Natural Science Foundation of China (11401008; 61672001; 61572035; 61402011) and China Postdoctoral Science Foundation (2016M592030). |
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| ON THE SUM OF k-POWER OF ALL DISTANCES IN BIPARTITE GRAPHS |
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GENG Xian-ya1, ZHAO Hong-jin1, XU Li-li2
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1.School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, China;2.School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
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| 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. |
| Key words: bipartite graph diameter extremal graph |
