The Energy Of Unicyclic Graphs With A Perfect Matching

In this thesis, we investigate the energy of connected unicyclic graph with a perfect matching, where possess vertices and edges. In Chapter two, the minimal energy graph for this kind of graphs in some cases is obtained. In the molecular orbital theory, the molecule of the conjugated hydrocarbons considered generally can be represented in carbon-atom skeleton graph, the character of this kind of graphs is that all vertices have degree no greater than three and have a perfect matching. In chapter three, the energy of the graphs whose largest degrees do not exceed three is further studied, and the graphs with minimal energy for this kind of graphs in some cases are determined. All the results in the thesis are deduced in the following way: Firstly, we compare the matching numbers of the graphs involved; Secondly, we compare the absolute values of the coefficients of the characteristic polynomials of the graphs.