Spanning Trees and Their Relations in Galois Covers
Abstract
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 Vallières. 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.
Fields of Study & Subjects
Graph theory and applications
Finite Group Theory Research
Analytic Number Theory Research
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 4
- Publication date
- 23 January 2026
- Language
- EN