Research On Distance Signless Laplacian Spectral Radius Of Uniform Hypergraphs

Graph theory is a branch of graph theory that studies the structure of relations in binary relations of discrete objects,and algebraic graph theory is a branch of graph theory that studies the properties of graphs by studying the algebraic properties of their correlation matrices.Hypergraphs are natural general extension of ordinary graphs.Compared with ordinary graph,hypergraphs can more accurately describe the relationship between multiple related objects.The eigenvalue of the distance matrix of ordinary graphs is caused by a data communication problem studied by Graham and Pollack in 1971,which has been extensively studied,among which the distance spectral radius has received extensive attention.Balaban and Ciubotariu et al.proposed using the distance spectral radius as the molecular descriptor of the graph.Compared with the distance spectral radius which has been studied more,the distance signless Laplacian spectral radius of distance was proposed in 2013.Since then,many scholars have begun to explore and study the distance signless Laplacian spectral radius of distance in graphs.In this thesis,we study the effect of two types of graft transformations on the distance spectral radius of connected k-uniform hypergraphs containing at least one cycle,determine the unique k-uniform uni cyclic hypergraphs of fixed edges with minimum distance signless Laplacian spectral radius.We study two graft transformations which decrease the distance signless Laplacian spectral radius of k-uniform bicyclic hypergraphs.At the same time,a bound is given for the distance signless Laplacian spectral radius of several k-uniform bicyclic hypergraphs.Finally,a 3-uniform bicyclic hypergraph with minimum distance signless Laplacian spectral radius is determined.