9 citations · 54 across the 26 of their papers we have counts for
8 papers · 1 filter
Alternating Walk/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato
We consider the alternating zeta function and the alternating -function of a graph , and express them by using the Ihara zeta function of . Next, we define a generalized a…
Metzler/Zeta Correspondence
Yusuke Ide, Takashi Komatsu, Norio Konno +1
We present an explicit formula for the determinant on the Metzler matrix of a digraph . Furthermore, we introduce a walk-type zeta function with respect to this Metzler matrix o…
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…
A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice
Takashi Komatsu, Norio Konno, Iwao Sato
Chinta, Jorgenson and Karlsson introduced a generalized version of the determinant formula for the Ihara zeta function associated to finite or infinite regular graphs. On the other…
The limit theorem with respect to the matrices on non-backtracking paths of a graph
Takehiro Hasegawa, Takashi Komatsu, Norio Konno +4
We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the th moments of the arcsine law…
Zeta functions with respect to general coined quantum walk of periodic graphs
Takashi Komatsu, Norio Konno, Iwao Sato
We define a zeta function of a graph by using the time evolution matrix of a general coined quantum walk on it, and give a determinant expression for the zeta function of a finite…