The Wiener Index Of Trees With Fixed Diameter

Wiener index was proposed in 1947 by the chemist Harold Wiener, as an important topological index in the study of quantum chemistry. Graph theory has important application in the Wiener index problem.In 2008,Sujuan Wang, Xiaofeng Guo proved: all the trees of order n and diameter d, the tree with minimum Wiener index in n,dT,let n,dT be the tree consisting of a path 0 1...dP ?v v v with other independent vertices adjacent to the center of n,dT.In 2006, Wagner derived the Wiener index formula of the tree with order number n and the diameter four, and prove the maximum22 n ?2n n ?n ?o( n);In this paper, firstly we give the largest Wiener index of the tree with diagram n ?4 ?d ?n ?2.Secondly deduce the tree general Wiener index equation with diameter 5, and discuss reaches the maximum figure some properties. Then using Lagrange analysis prove the upper bounds of the equation. According to the above conclusions and using computer aided calculation, give the maximum Wiener index, and the maximum figure with the tree of diameter of 5, vertices n ?40.