Year: 2025
Type: preprint
Abstract: This paper studies the relation among the number of spanning trees of intermediate graphs in a Galois cover, building on results for $(\mathbb{Z}/2\mathbb{Z})^m$-covers previously established by Hammer, Mattman, Sands, and Valli\`{e}res. We generalize their results to arbitrary finite Galois covers. Using the Ihara zeta function and the Artin--Ihara $L$-function, we prove two formulas which are graph-theoretic analogues of Kuroda's formula and the Brauer--Kuroda relations in algebraic number theory. Furthermore, we prove that a spanning tree formula does not exist if the Galois group is cyclic.
Source: arXiv (Cornell University)
Author: Mizuno, Kosuke
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979275859
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