Generalized Randi (?) The Maximization Problem Of The Indicators On The Tree Diagram

In the chemistry study, certain defined indicators of hydrocarbons could reflect some important physical and chemical properties easily and intuitively. Randic index is one of such indicators. The research of extremal problem of Randic index does not only have important significance in mathematics, but plays an important role for chemistry study.This paper is about the tree with maximum general Randic index. The general Randic index R_-α(G) of a simple graph G, is defined as the sum of the weights (d(u)d(v))^-α of all edges uv of G, where d(u) denotes the degree of a vertex u in G. Most of the maximization problems about trees have been solved, left only the maximum value of R_-α whenα∈(1/2,2) is undetermined, this paper will discuss some part of this problem.In chapter 1, the background, significance and some related results so far will be introduced.In chapter 2, we will study the maximum value of the general Randic index R_-α, whereα∈(α₀,2).In chapter 3, we will present an important property of the Max Tree which has the maximum general Randic index R_-α, whereα∈(1,2).In chapter 4, we will summarize all the conclusions and will bring forward a conjecture of the structure of the Max Tree, besides we give a method which might be helpful in completely solving this problem.