Spectral Moments Of Bicyclic Graphs

The aim of this thesis is to present several results on spectral moments of bicyclic graphs. It is made up of four parts.Firstly, Section One is an introduction to the background of the research and the results we gain in this thesis. Section Two is about some concepts and lemmas involved as follows. Section Three provides the mainly results on the spectral moment of bicycle graphs and its lexicographical order.In Section Three, the classification of bicyclic graphs is firstly presented according to the different positons of its two bicycles , and then the general regularity of calculation to spectral moments of bicyclic graph is discussed . The final part comes to some regular conclusions of spectral moment order which based on the parameter change of bicyclic graphs.In addition, diagrams of the 221 bicyclic graphs on eight vertices are given in Appendix which are ordered lexicographically by spectra moments, and for each graph from Table 1 the degree sequence and the first six spectral moments are given in Table 2.