Property And Application Of The Chromatic Orbit Polynomial

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.