# A remark on zeta functions of finite graphs via quantum walks

@article{Higuchi2014ARO, title={A remark on zeta functions of finite graphs via quantum walks}, author={Yusuke Higuchi and Norio Konno and Iwao Sato and Etsuo Segawa}, journal={Pacific Journal of Mathematics for Industry}, year={2014}, volume={6}, pages={1-8} }

From the viewpoint of quantum walks, the Ihara zeta function of a finite graph can be said to be closely related to its evolution matrix. In this note we introduce another kind of zeta function of a graph, which is closely related to, as to say, the square of the evolution matrix of a quantum walk. Then we give to such a function two types of determinant expressions and derive from it some geometric properties of a finite graph. As an application, we illustrate the distribution of poles of this…

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