On The Spectral Radii Of γ Uniform Hypergraphs

The spectra of graph theory is a very important research area in algebra graph theory, which study on algeric properties and applications about associated matrices of graphs, such as the Adjacency matrix, the Incidence matrix, the Lapidar-ian matrix, the sinless lapidarian matrix and so on. In this paper graphs which are discussed are simple connected.Hypergraph is a generalization of the graph,the spec-tral of hypergraph has attract the researcher of graph’s attention.Before 2005,the research on spectral of hypergraph based on the matrix,but hypergraph and matrix is not one to one correspondence,the matrix is uncertain.From 2004,liqunQi of Hong Kong defines the tensor spectral,gongqingZhang and liqunQi depict some properties of the tensor spectral,these for reseaching on the tensor spectral lay a theoretical foundation and framework.Therefore, we will investigate the study of the spectral radius of hypergraph with given number of branching vertices and r uniform linear hypergraph. This paper is divided into three parts and the main structure of the article is as follows.In chapter 1:we introduce the fundamental concepts and properties of graphs and hypergraphs, also the domestic and foreign researching situations.In chapter 2:In this chapter, we study the spectral radii of k-uniform hy-pergraphs on the operation of splitting a vertex and some extremal problems of spectral radii of 3-uniform supertrees. We prove that Tn,k is 3-uniform supertrees with the maximum spectral radii among all 3-uniform supertrees with n vertices and k pendent edges. We also show that Tnd is 3-uniform supertrees with the maximum spectral radii among all 3-uniform supertrees with n vertices and diameterd and prove that H is a r uniform hypergraph with m edges,every edge has p vertices in common,(1≤p≤r, and p is positive integer), then the spectral radius of H is ρ(H)=(r-1)!(?)mp.In chapter 3:we study the spectral of trees with given number of branching vertices.