The quaternionic second weighted zeta function of a graph and the Study determinant
Combinatorics
2016-04-01 v2
Abstract
We establish a generalization of the second weighted zeta function of a graph to the case of quaternions. For an arc-weighted graph whose weights are quaternions, we define the second weighted zeta function by using the Study determinant that is a quaternionic determinant for quaternionic matrices defined by Study. This definition is regarded as a quaternionic analogue of the determinant expression of Hashimoto type for the Ihara zeta function of a graph. We derive the Study determinant expression of Bass type and the Euler product for the quaternionic second weighted zeta function.
Keywords
Cite
@article{arxiv.1601.07760,
title = {The quaternionic second weighted zeta function of a graph and the Study determinant},
author = {Norio Konno and Hideo Mitsuhashi and Iwao Sato},
journal= {arXiv preprint arXiv:1601.07760},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1507.06761