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The Ihara expression for generalized weighted zeta functions of Bartholdi type on finite digraphs
Ayaka Ishikawa, Hideaki Morita, Iwao Sato
The Ihara expression of a weighted zeta function for a general finite digraph is given. It unifies all the Ihara expressions obtained for known zeta functions for finite digraphs.…
A Generalized Grover/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato +1
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 Grove…
The trace formula with respect to the twisted Grover matrix of a mixed digraph
Takashi Komatsu, Sho Kubota, Norio Konno +1
We define a zeta function woth respect to the twisted Grover matrix of a mixed digraph, and present an exponential expression and a determinant expression of this zeta function. As…
The scattering matrix with respect to an Hermitian matrix of a graph
Takashi Komatsu, Norio Konno, Iwao Sato
Recently, Gnutzmann and Smilansky presented a formula for the bond scattering matrix of a graph with respect to a Hermitian matrix. We present another proof for this Gnutzmann and…
Zeta functions of periodic graphs derived from quantum walk
Takashi Komatsu, Norio Konno, Iwao Sato
We define a zeta function of a finite graph derived from time evolution matrix of quantum walk, and give its determinant expression. Furthermore, we generalize the above result to…
A zeta function related to the transition matrix of the discrete-time quantum walk on a graph
Norio Konno, Iwao Sato, Etsuo Segawa
We present the structure theorem for the positive support of the cube of the Grover transition matrix of the discrete-time quantum walk (the Grover walk) on a general graph und…