树图与单圈图的线图的Hyper-Wiener指数

Hyper-Wiener Index of Line Graphs of Trees and Unicyclic Graphs

主要考虑了线图的hyper-Wiener指数,分别得到了树图和单圈图的线图的hyper-Wiener指数的上下界及取得上下界的极图.

In a connected graph G,the distance d（u,ν）is the length of the shortest path from u to ν.The hyper-Wiener index of G,WW（G）,is defined as 1/2∑u,ν∈V（G）d（u,ν）＋1/2∑u,ν∈V（G）d^2（u,ν）,with the summation going over all pairs of vertices in G.In this paper,we mainly consider the hyper-Wiener index of line graph.The upper and lower bounds on hyper-Wiener indices of line graphs of trees and unicyclic graphs are obtained,respectively.