具有第3大Wiener指数的有向图  

The Digraphs with the Third Maximum Wiener Index

作　　者：江云涛 高玉斌[1] 赵玉杰 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《江西师范大学学报（自然科学版）》2017年第5期518-523,共6页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11071227)资助项目

摘　　要：通过有向图的Wiener指数,可以给有向网络的平均距离和节点的中介中心性赋有限的值,进而应用于大规模网络的分析.在所有n阶有向图中,有向圈C→n能取到极大Wiener指数,C→+n能取到第2大Wiener指数,利用反证法及分类讨论法对有向图的Wiener指数进行研究,得出了具有第3大Wiener指数的有向图,并刻画了相应的极图.The extension to digraphs of Wiener index could be applicable in the topics of directed large networks,particularly because with this measure,one assigns finite values to the average distance and betweenness centrality of the nodes in a directed network. It is shown that among digraphs on n vertices,the directed cycle C→nachieves the maximum Wiener index,and C→ ＋nachieves the second maximum Wiener index. The Wiener index of directed graphs is studied by using reduction to absurdity and discussing method. The directed graphs with the third largest Wiener exponent are obtained and depict the corresponding extreme graphs.

关 键 词：WIENER指数 有向图 平均距离 网络 

分 类 号：O157.5[理学—数学]