与图Zeta函数相关的一个函数的导数值

设G是含有n个顶点和ε条边的图，G的Zeta函数可以表示为ZG(u)=(1-u2)n-ε/f(u)，其中f(u)=det(I-uA (G)+u2(D (G)-I))，A(G)与D (G)分别表示G的邻接矩阵与度对角矩阵。分别利用正则图的TU子图的权重ω和二部图的顶点n和边数ε来表示相应的f′(-1)的值。

The Derivative of a Function Related to the Zeta Function of Graph

Suppose that G is a graph with n vertices and εedges,the Zeta function of G could be expressed as ZG(u)=(1-u2)n-ε/f(u),where f(u)=det(I-uA (G)+u2(D (G)-I)),A(G) and D (G) are the adjacency matrix and diagonal matrix of degrees of G.In this paper,we use the weights of the TU -subgraphs of regular graph and the vertices number n and the edges number εof bipartite graph to express f′(-1),respectively.