图的Hyper-Wiener指数的综述(英文)

Recent Results on the Hyper- Wiener Index of Graphs

设G是一个图.G的顶点u和v的距离是u和v之间最短路的长度.Wiener指数是G中所有无序顶点对之间距离之和,而Hyper-Wiener指数定义为WW(G)=?∑u,v∈V(G)d(u,v)+?∑u,v∈V(G)d2(u,v),式中的和取遍G的所有顶点对.本文总结了图的Hyper-Wiener指数的最近结论.

Let G be a graph. The distance d（u,v） between the vertices u and v of the graph G is equal to the length of a shortest path that connects u and v. The Wiener index W（G） is the sum of all distances between vertices of G,whereas the Hyper - Wiener index WW（G） is defined as WW（G）=1/2∑u,v∈V（G）d（u,v）＋1/2∑u,v∈V（G）d2（u,v）,with the summation going over all pairs of vertices in G. In this paper, we survey recent results on the Hyper - Wiener index of graphs.