Research On Digraphs With Large Maximum Wiener Index

Topological index is one of the most important research topics in chemical graph theory.It has plenty of applications in the molecular structure of the chemistry,and its research and development prospect is broad.In this paper,first of all,we give a definition of the Wiener index for the undirected graph and the directed graph.Secondly,we research the Wiener index with a directed graph of the great direction,and summarize the extreme values and the corresponding extreme graphs of the digraph with largest and second largest Wiener index.Besides,the digraph and extreme values of the third largest Wiener index are also given.In the first chapter,we introduce the historical of the Wiener index,and give some basic knowledge,relevant conclusions,and the main conclusions of this paper.In the second chapter,firstly we give some important thorems of the Wiener index of the directed graph and summarize the extreme values and the corresponding extreme graphs with the largest and the second largest Wiener index.The third largest Wiener index and the corresponding extreme graph is obtained by using methods including classified discussion,proof by contradiction and so on.