The Research Of Several Problems About Hypergraphs In Algebraic Method

Some results of the research about graph in algebraic method were given by Godsil and Royle. For example: The relation between the connectedness of transpositions graphΓand the generating set of symmetric group of order n ; Some results of the automorphism group of graph; Some results of the fractional colouring of graph and fractional clique of graph; Some results of the research about the colouring of graph by homomorphism of graph and so on.Hypergraph has the most common and the most complicated construction in discrete mathematics,it is generation of graph,but it can not be easily generalized to hypergraph for some definitions and some conclusions in graph. This paper discuss the hypergraph by algebraic method, and some results of graph in the first dialogue be generalized to hypergraph. The structure of this paper is:The first chapter is an introduction. In this chapter, the found and development of hypergraph and algebraic graph theory are introduced. Some definitions and symbols were given. For example: the automorphism group of hypergraph, fractional colouring of hypergraph, fractional clique of hypergraph and homomorphism of hypergraph and so on. It correspond with definition of the automorphism group of graph,fractional colouring of graph,fractional clique of graph and homomorphism of graph and so on.The connectedness of 3-uniform hypergraph were discussed in the second chapter. The relation between the connectedness of 3-uniform hypergraph and the generating set of alternative group of order n and the characters of unconnected 3-uniform hypergraph were given.The automorphism group of hypergraph by discussing in the third chapter. Some results were given by the automorphism group of hypergraph for the degree of vertex of hypergraph, the distance between two edges of hypergraph and the complement of r-uniform hypergraph and so on.The colouring of hypergraph by discussing in the fourth chapter. Some results of fractional colouring of hypergraph, fractional clique of hypergraph and the colouring of hypergraph by homomorphism of hypergraph were griven.