The graph zeta functions with respect to the group matrix of a finite group

2025/03/21 by Miezaki, Tsuyoshi, Sato, Iwao
#05C50 #15A15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.16821

Abstract

In this paper, we present formulas for the edge zeta function and the second weighted zeta function with respect to the group matrix of a finite abelian group Γ. Furthermore, we give another proof of Dedekind Theorem for the group determinant of Γ by the decomposition formula for a matrix of a group covering of a digraph. Finally, we treat the weighted complexity of the complete graph with entries of the group matrix of Γ as arc weights.

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