图覆盖的特征多项式

Characteristic Polynomials of Covering Graphs

依据图覆盖与电压图理论的关系,运用群表示理论对电压图做进一步研究,从而给出了有限图覆盖(可能为非正则)的特征多项式的分解表达式,以及有限图覆盖的Lap lace矩阵的特征多项式的表达式,借助于群论实现了对图的不变量的研究,得到的表达式为进一步研究图提供了依据。

Based on the relationship between the covering graph theory and the voltage graph theory, using the representation of finite groups to study the voltage graph further, this paper explicits decomposition formulas for the characteristic polynomial of a possibly irregular covering of a finite graph and a Laplace Matrix of a possibly irregular covering of a finite graph is obtained. With the help of the theory of group, the study of the invariants of graph is carried out. The expression gained offers the basis which is used to study graph further.