Sorting Graphs With Given Diameter By Spectral Radius

The spectral radius can reflect some properties of a graph, and it is also a popular subject of graph theory. Some good methods and beautiful results have already appeared in determining the boundaries of spectral radius and comparing some graphs etc. In this thesis, we give some new results in studying the spectral radius, especially the results between trees and unicyclic graphs.Some graphs have special structures. In the study of the characteristic polynomials of these graphs, we summarize the technique of finding out a graph with the same spectral radius. By using these graphs, it is possible to compare the spectral radius of some graphs. Although not every graph can have these structures, it is so efficient in the comparison of the graphs with given diameter D = n - k.