| Combinatoric enumeration and the coloring of graph are important parts of combinatoric mathematics and graph theory,and Polya theorem and the chromatic polynomial are major methods of studying them.In[3],Professor Du Qingyan put the both together,and gave the definitions of the chromatic orbit and the chromatic primitive polynomial,also introduced the conceptions of P-graph and SC-graph.In this thesis,we study the properties of chromatic orbit polynomials of P-graph and the primitive chromatic polynomial of P-graph and SC-graph.The main results are as follows:1.The properties of the chromatic orbit polynomial and the primitive chromatic polynomial of P-graph are introduced;2.When the group P is given,how to compute the primitive chromatic polynomial of P-graph;3.Further results are discussed about the concrete computation formulas of necklace;4.Some instances of the primitive chromatic polynomial of P-graph applied in chemistry are given. |
