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A new generalized Bartholdi zeta function for a digraph. (English) Zbl 1461.05132

Summary: We define a new generalized Bartholdi zeta function of a digraph \(D\), and give a determinant expression of it. We present a decomposition formula for the new generalized Bartholdi zeta function of a group covering of \(D\). Furthermore, we introduce a new generalized Bartholdi \(L\)-function of \(D\), and give a determinant expressions of it. As an application, we present a decomposition formula for the new generalized Bartholdi zeta function of a group covering of \(D\) by its new generalized Bartholdi \(L\)-functions.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C20 Directed graphs (digraphs), tournaments
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
15A15 Determinants, permanents, traces, other special matrix functions
11M41 Other Dirichlet series and zeta functions
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References:

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