Kazakov-Migdal model on the graph and Ihara zeta function by So Matsuura, Kazutoshi Ohta

“…Abstract We propose the Kazakov-Migdal model on graphs and show that, when the parameters of this model are appropriately tuned, the partition function is represented by the unitary matrix integral of an extended Ihara zeta function, which has a series expansion by all non-collapsing Wilson loops with their lengths as weights. …”
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Zeta functions from graphs by Simon Davis

“…The existence of a similarity transformation of the diagonal matrix given by a specified set of eigenvalues to an adjacency matrix of a graph is proven, and the method yields a set of finite graphs with eigenvalues determined approximately by a finite subset of the poles of the Ihara zeta function.…”
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Zeta functions from graphs by Simon Davis

“…The existence of a similarity transformation of the diagonal matrix given by a specified set of eigenvalues to an adjacency matrix of a graph is proven, and the method yields a set of finite graphs with eigenvalues determined approximately by a finite subset of the poles of the Ihara zeta function. Keywords: Graph, Zeta function, Adjacency matrix, Eigenvalues…”
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