Research On The Spectral Radius Of Uniform Weighted Hypergraph

Hypergraphs are a generalization of graphs,which can accurately represent the complex multivariate relationships between objects in practical problems,while graphs cannot fully characterize such problems.There is a natural correspondence between uniform hypergraphs and tensors,researchers use the theory of tensors to characterize the construction and characteristics of uniform hypergraphs.Spectral hypergraph theory is a natural extension of spectral graph theory.In the research field of combinatorics and graph theory,the spectral hypergraph theory is an important research direction,and it is widely used in applied physics,operations research and other fields.In the theory of hypergraph of spectrum,the study on the adjacency tensor,Laplacian tensor and signless Laplacian tensor spectrum of uniform hypergraph has received extensive attention from scholars.In this dissertation,we first study the spectral radius of the adjacency tensor of a weighted hypergraph,the upper bound of the radius of the weighted hypergraph is given by using the average 2 degree of the uniformly weighted hypergraph and the weighted degree sequence of the vertices of the uniformly weighted hypergraph.In addition,the dissertation studies the bounds of the spectral radius of the signless Laplacian tensor corresponding to the weighted hypergraph,and the bounds of the spectral radius of the signless Laplacian tensor of uniformly weighted connected hypergraphs and uniformly linearly weighted connected hypergraphs are given through the weighted degree sequence of vertices.Finally,the bounds of the improved form of the spectral radius of the signless Laplace tensor are given.