Zeta functions of finite Schreier graphs and their zig-zag products
نویسندگان
چکیده
منابع مشابه
Zeta Functions of Finite Graphs
Poles of the Ihara zeta function associated with a finite 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 theorem on the determinant expression of the zeta function and Hashimoto’s theorems on the pole at u = 1.
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we investigate two constructions - the replacement and the zig-zag product of graphs - describing several fascinating connections with combinatorics, via the notion of expander graph, group theory, via the notion of semidirect product and cayley graph, and with markov chains, via the lamplighter random walk. many examples are provided.
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2016
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498817501511