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383
Zeta functions of finite graphs
 J. MATH. SCI. UNIV. TOKYO
, 2000
"... Poles of the Ihara zeta function associated with a finite graph are described by graphtheoretic quantities. Elementary proofs based on the notions of oriented line graphs, PerronFrobenius operators, and discrete Laplacians are provided for Bass’s theorem on the determinant expression of the zeta f ..."
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Cited by 41 (1 self)
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Poles of the Ihara zeta function associated with a finite graph are described by graphtheoretic quantities. Elementary proofs based on the notions of oriented line graphs, PerronFrobenius operators, and discrete Laplacians are provided for Bass’s theorem on the determinant expression of the zeta
Quantum chaos on discrete graphs
 J. Phys. A
"... Adapting a method developed for the study of quantum chaos on quantum (metric) graphs [1], spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph, and obtaining f ..."
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Cited by 19 (4 self)
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Adapting a method developed for the study of quantum chaos on quantum (metric) graphs [1], spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph, and obtaining
Zeta Functions of weighted graphs and covering graphs
, 2007
"... We find a condition for weights on the edges of a graph which insures that the Ihara zeta function has a 3term determinant formula. Then we investigate the locations of poles of abelian graph coverings and compare the results with random covers. We discover that the zeta function of the random cove ..."
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Cited by 5 (0 self)
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We find a condition for weights on the edges of a graph which insures that the Ihara zeta function has a 3term determinant formula. Then we investigate the locations of poles of abelian graph coverings and compare the results with random covers. We discover that the zeta function of the random
Generation of Isospectral Graphs
 J. GRAPH THEORY
, 1999
"... We discuss a discrete version of Sunada's Theorem on isospectral manifolds which allows to generate isospectral simple graphs, i.e. nonisomorphic simple graphs whichhave the same Laplace spectrum. We also consider additional boundary conditions and Buser's transplantation technique appl ..."
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Cited by 5 (1 self)
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We discuss a discrete version of Sunada's Theorem on isospectral manifolds which allows to generate isospectral simple graphs, i.e. nonisomorphic simple graphs whichhave the same Laplace spectrum. We also consider additional boundary conditions and Buser's transplantation technique
The Dirac operator of a graph
, 2013
"... Abstract. We discuss some linear algebra related to the Dirac matrix D of a finite simple graph G = (V, E). ..."
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Cited by 6 (5 self)
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Abstract. We discuss some linear algebra related to the Dirac matrix D of a finite simple graph G = (V, E).
Isospectrality conditions for regular graphs
, 1998
"... Let k ≥ 3 be an integer and let Γ be a kregular, undirected graph with a finite number N of vertices. If A is an adjacency matrix for Γ, then the multiset {λ1, λ2,..., λN} of eigenvalues of A is called the spectrum of the graph Γ. Since Γ is undirected, A is symmetric and so its eigenvalues are ..."
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Cited by 3 (1 self)
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Let k ≥ 3 be an integer and let Γ be a kregular, undirected graph with a finite number N of vertices. If A is an adjacency matrix for Γ, then the multiset {λ1, λ2,..., λN} of eigenvalues of A is called the spectrum of the graph Γ. Since Γ is undirected, A is symmetric and so its eigenvalues are
Results 1  10
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383