Trees Preserving Wiener Index In Some Classes Of Graph

It's well known that a topological index is a map from the set of chemical comp-ounds represend by molecular graphs to the set of real numbers. Many topological in-dices are closely correlated with some physico-chemical characteristics of the underl-ying compounds, therefore, it plays an important role in the chemical, medical, phar-maceutial and many other aspects. There are more than one hundred kinds are availa-ble. Wiener index is well-known as the first molecular topological index in the chem-ical industry, which is made by the chemist Harold Wiener in 1947, and he gived the formula to calculate it.Once proposed, the Wiener index has been widely explored and studied, series of results have emerged. Preserving Wiener index trees is one dirction of the Wiener index, it was first propposed in 2001. Given a connected graph G, the existence of insurance and how to find the preserving Wiener index trees in it are the two most critical issues.This article includes four chapters.In Chapter one, we introduce a brief background of the graph theory, Wiener ind-ex and Preserving Wiener index trees, the problem and the result we obtained in this thesis.In Chapter two, we give the preserving Wiener index trees of Join-graph Pm∨P2k+1.In Chapter three, we give the preserving Wiener index trees of two kinds of Dou-ble-wheels graphs.In Chapter four, we give the summary and outlook of the preserving Wiener index trees in connected graphs.