Zeta Functions of Finite Graphs
Zeta Functions of Finite Graphs
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发表时间：
2000
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通讯作者：
M. Kotani;T. Sunada
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文献类型：
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作者：
M. Kotani;T. Sunada
本文用图论量描述了有限图的Ihara zeta函数的极点。基于定向线图、Perron-Frobenius算子和离散Laplacian算子的概念，给出了Bass定理关于zeta函数的行列式表达式和Hashimoto定理关于u =1极点的初等证明.
Poles of the Ihara zeta function associated with a fi- nite graph are described by graph-theoretic quantities. Elementary proofs based on the notions of oriented line graphs, Perron-Frobenius operators, and discrete Laplacians are provided for Bass's theoremon the determinant expression of the zeta function and Hashimoto's the- orems on the pole at u =1 .