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math.CO2022
A family of quantum walks on a finite graph corresponding to the generalized weighted zeta function
Ayaka Ishikawa
This paper gives the quantum walks determined by graph zeta functions. The result enables us to obtain the characteristic polynomial of the transition matrix of the quantum walk, a…
math.CO2022
The Ihara expression of a generalization of the weighted zeta function on a finite digraph
Ayaka Ishikawa
We define a new weighted zeta function for a finite digraph and obtain its determinant expression called the Ihara expression. The graph zeta function is a generalization of the we…
math.CO2022
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.…