【摘要】 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-u A(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和二部图的顶点数n和边数ε来表示相应的f’(-1)的值。更多还原

【Abstract】 Suppose that G is a graph with n vertices and ε edges,the Zeta function of G could be expressed as ZG( u) =( 1- u2)n- ε/ f( u),where f( u) = det( I- u A( 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 ε of bipartite graph to express f’(- 1),respectively.更多还原