The quaternionic weighted zeta function of a graph
Combinatorics
2015-09-28 v2
Abstract
We establish the quaternionic weighted zeta function of a graph and its Study determinant expressions. For a graph with quaternionic weights on arcs, we define a zeta function by using an infinite product which is regarded as the Euler product. This is a quaternionic extension of the square of the Ihara zeta function. We show that the new zeta function can be expressed as the exponential of a generating function and that it has two Study determinant expressions, which are crucial for the theory of zeta functions of graphs.
Cite
@article{arxiv.1507.06761,
title = {The quaternionic weighted zeta function of a graph},
author = {Norio Konno and Hideo Mitsuhashi and Iwao Sato},
journal= {arXiv preprint arXiv:1507.06761},
year = {2015}
}