论文标题
广义的Grover/Zeta对应关系
A Generalized Grover/Zeta Correspondence
论文作者
论文摘要
我们引入了图形的广义Grover矩阵，并为其特征多项式提供了明确的公式。作为推论，我们给出了常规图的广义格罗矩阵的光谱。接下来，我们将图$ g $的zeta函数和广义zeta函数相对于其广义的格罗弗矩阵作为IHARA ZETA函数的类似物，并为其Zeta函数提供了顶点传播图的显式公式。作为应用，我们通过积分来表达有限顶点传播常规图的广义Zeta函数的限制。此外，我们将有限托里家族的广义Zeta函数限制为整体表达。
We introduce a generalized Grover matrix of a graph and present an explicit formula for its characteristic polynomial. As a corollary, we give the spectra for the generalized Grover matrix of a regular graph. Next, we define a zeta function and a generalized zeta function of a graph $G$ with respect to its generalized Grover matrix as an analog of the Ihara zeta function and present explicit formulas for their zeta functions for a vertex-transitive graph. As applications, we express the limit on the generalized zeta functions of a family of finite vertex-transitive regular graphs by an integral. Furthermore, we give the limit on the generalized zeta functions of a family of finite tori as an integral expression.
