Pólya公式与色轨道多项式(英文)

Pólya′s Formula and Chromatic Orbit Polynomials

色轨道多项式是色多项式与 Pólya计数公式的推广 .本文定义了色轨道多项式及其相应的概念如 P-图 ,SC-图等 ,给出了色轨道多项式的表达式和计算方法 ,讨论了色轨道多项式的基本性质 .作为它的一个应用 。

The chromatic orbit polynomials of graphs presented in this paper are integration and generalization of Pólya′s Formula and the chromatic polynomials of graphs.Relevant new notions such as the P graph and SC graph of graph are also introduced.The expressions of the chromatic orbit polynomials of graphs are given.Some elementary properties of chromatic orbit polynomials of graphs are established.The necklace problem is proposed as an instance to illustrate these notions and the solutions of the necklace problem are given by explicit formulas.