Discussion On Some Properties Of Line Graph Of The Hypergraph

The line graph transformation is the most widely studied one among all graph transformations. The study of line graph has produced a lot of results, such as the relationship of the path graph and the line graph, the line graph and the crossing mumbers of some typical graphs classes and so on. With the development of graph theory,graph theory has been extended to the hypergraph. The graph is 2-uniform hypergraph from the point of hypergraph,and it is a special structure of hypergraph. The line graph,as the most extensive transformation of a graph be studied,can be extended to hypergraph. So the study area of the line graph can be extended,and the line graph transformation can play a greater role in a wider area.This paper discusses some properties in hypergraph and the line graph of hypergraph.Chapter 1 Introduction.This chapter mainly introduces the development of the hypergraph and the line graph .Chapter II basic concepts and basic lemmas.This chapter gives definitions and concepts in the hypergraph be used in this paper,and give some lemmas in graph and line graph.Chapter III some properties in hypergraph and line graph.This chapter is divided into three sections, and extends the basic lemma in the second chapter to 3-uniform hypergraph,r-uniform hypergraph and arbitrary hypergraph,and gives proofs. Chapter IV references.This paper gives out all the references be used in this paper. Chapter V acknowledgement.Thanks for the teachers and the students who give me help during the period of the completion of my paper.