The Minimal Signless Laplacian Spectral Radius Of Graphs With Grven Diameter

The theory of the spectral radius of graphs is one important field in graph theory andmathematical combination theory, including spectral radius, Laplacian spectral radius,signless Laplacian spectral radius and regular Laplacian spectral radius. In the fields ofquantum chemistry, physics, computer science, communication network and informationscience and technology it is widely used. In the paper we make use of algebraic method andGeometric method and study the signless Laplacian spectral radius of graphs, especially in theend we give some signless Laplacian spectral radius of graphs with given diameter.Main content as follows:(1) Classify and summarize the results about spectral radius of graphs.(2) Study and get the minimal signless Laplacian spectral radius of graphs with givendiameter d∈{n-3,n-2,n-1}.(3) Study and get the minimal signless Laplacian spectral radius of graphs with givendiameter d∈{1,2,3}.(4) Study and get the minimal signless Laplacian spectral radius of graphs with givendiameter n-4.