Geodesic
A new determinant expression for the weighted Bartholdi zeta function of a digraph
Iwao Sato1 ; Hideo Mitsuhasi2 ; Hideaki Morita3
1Oyama National College of Technology
2Oyama National College of Technology Oyama, Tochigi 323-0806, JAPAN
3Division of System Engineering for Mathematics Muroran Institute of Technology Muroran, Hokkaido 050-8585, JAPAN
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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We consider the weighted Bartholdi zeta function of a digraph $D$, and give a new determinant expression of it. Furthermore, we treat a weighted $L$-function of $D$, and give a new determinant expression of it. As a corollary, we present determinant expressions for the Bartholdi edge zeta functions of a graph and a digraph.
DOI : 10.37236/2649
Classification : 05C50, 05C20, 11M99, 15A15
Mots-clés : weighted Bartholdi zeta function, digraph, covering, \(L\)-function

Iwao Sato  1   ; Hideo Mitsuhasi  2   ; Hideaki Morita  3

1 Oyama National College of Technology
2 Oyama National College of Technology Oyama, Tochigi 323-0806, JAPAN
3 Division of System Engineering for Mathematics Muroran Institute of Technology Muroran, Hokkaido 050-8585, JAPAN 
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     title = {A new determinant expression for the weighted {Bartholdi} zeta function of a digraph},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {1},
     doi = {10.37236/2649},
     zbl = {1266.05083},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2649/}
}
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Iwao Sato; Hideo Mitsuhasi; Hideaki Morita. A new determinant expression for the weighted Bartholdi zeta function of a digraph. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2649

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