Spectral Extremum Problems Of Uniform Hypergraphs With Fixed Parameters

Hypergraphs are often used as a successful tool to describe structures in discrete mathematics,computer science,and other fields.Hypergraph theory and its parameter research are important research topics in hypergraph theory.The problem of spectral extrema of graphs originated from the problem proposed by Brualdi and Solheid in1986:to find the bound of the spectral radius of a given graph class and characterize its extreme graph with the maximum or minimum spectral radius.At present,the re-search in this area has also been successfully transferred to the research on the extreme value problem of hypergraphs.One of the hot research issues is the spectral extremum problem of hypergraphs with fixed hypergraph parameters,that is,how to determine the bounds of the hypergraph radius and characterize the extremum hypergraphs under given parameters?Accordingly,this paper studies three fixed hypergraph classes:One is to study the spectral extremum problem of a uniform hypergraph with a fixed diameter or number of cliques.By defining two new types of hypergraphs,the extreme hypergraph;with the largest hypergraph radius is determined in a consistent hypergraph with a fixed number of vertices and diameters,and a extreme hypergraph with the smallest hypergraph radius in a uniform hypergraph with a fixed number of vertices and cliques;The second is to study the spectral extremum problem of a unicyclic uniform hypergraph with a fixed diameter.By defining two types of unicyclic uniform hyper-graphs,and with the help of the spectral properties of these two types of unicyclic uniform hypergraphs,the spectral properties of hypergraph subdivision edges,and the influence of moving edges to change the hypergraph structure on the hypergraph ra-dius,The extremum hypergraph with the largest spectral radius is determined in a unicyclic uniform hypergraph of fixed diameter;The third is to study the minimum spectral extremum problem of uniform hyper-trees with fixed diameter d.First three subset classes of uniform hypertrees with fixed diameter d are defined,and the three classes of special hypertrees with fixed diameters are characterized respectively as having a small first [d/2]-1 the extreme hypergraph of the spectral radius,finally determines the extreme hypergraph with the smallest spec-tral radius for a uniform hypertree of a given diameter.