图的顶点矩阵加权Zeta函数

A Vertex Matrix-Weighted Zeta Function of a Graph

对于一个图,定义了它的顶点矩阵加权zeta函数,并给出了相对应的行列式表达式。之后定义了图的顶点矩阵加权L-函数。然后对于二部图给出了其顶点矩阵加权zeta函数和L-函数的具体形式。最后计算了二部图zeta函数的例子。

We define a vertex matrix-weighted zeta function of a graph, and give a determinant expression of it. Then we give the L-function in this weight. Furthermore, we define a vertex matrix-weighted zeta function of a bipartite graph, and give the determinant expression of zeta function and L-function of a bipartite graph. Finally, we give an example of the zeta function of a bipartite graph.