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arXiv · 1404.1553

A remark on zeta functions of finite graphs via quantum walks

Yu. Higuchi·N. Konno·I. Sato·E. Segawa
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Abstract

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 function comparing with those of the usual Ihara zeta function.

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Yu. Higuchi, N. Konno, I. Sato, E. Segawa. 2014-04-06. A remark on zeta functions of finite graphs via quantum walks. https://arxiv.org/abs/1404.1553

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