Expression Of Characteristic Polynomials Of A Class Of 3 Uniform Hypergraphs

With the development of big data science and artificial intelligence,many practical problems with huge amounts of data and complex relationships have emerged.Graphs cannot fully describe the characteristics of such problems,while hypergraphs can accurately represent the more complex objects in actual problems.Multiple relationships.Therefore,the research of hypergraph problem has become a hot field,and the characteristic polynomial of hypergraph is a basic problem in the study of hypergraph theory.The study of the representation of the characteristic polynomial of hypergraph is theoretically important.In recent years,the study of hypergraph characteristic polynomials has attracted the attention of many scholars.The hypergraph is a further development of the graph.If each edge in the hypergraph has k different vertexs,it is said to be a k uniform hypergraph.The spectrum of a hypergraph is the spectrum of its adjacency tensor.In the study of hypergraphs,the characteristic polynomial problem of uniform hypergraph adjacency tensors is a research hotspot in the field of hypergraph spectral theory.The characteristic polynomials of uniform hyperpaths,uniform hyperstars,and like star hypertrees have been given,and the above are all characteristic polynomials of acyclic hypergraphs.This paper mainly studies the characteristic polynomial problem of a class of k uniform hypergraphs with cycles.This paper presents the characteristic polynomials of a class of 3 uniform hypergraphs with cycles.The main results are as follows:For a power hypercycleC₃^（3）with 3 uniform three edges,Using the Poisson product formula of hypergraph,its characteristic polynomial is given;combined with the Poisson product formula of the hypergraph and the characteristic polynomial ofC₃^（3）,the concatenation formula of the characteristic polynomial of the 3 uniform power hypercycle C₃^（3）is given;Using the concatenation formula of this paper and the characteristic polynomials of hyperpaths,hyperstars and hypercycles,the exact representations of three characteristic polynomials of hypergraphs with cycles are given.