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arXiv · 1601.07760

The quaternionic second weighted zeta function of a graph and the Study determinant

Norio Konno·Hideo Mitsuhashi·Iwao Sato
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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.

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Norio Konno, Hideo Mitsuhashi, Iwao Sato. 2016-03-31. The quaternionic second weighted zeta function of a graph and the Study determinant. https://arxiv.org/abs/1601.07760

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