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  3. Zeta Functions of Graphs
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2013
      November 2010
      ISBN:
      9780511760426
      9780521113670
      DOI:
      https://doi.org/10.1017/CBO9780511760426
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.53kg, 252 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
      Series:
      Cambridge Studies in Advanced Mathematics (128)
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
    Series:
    Cambridge Studies in Advanced Mathematics (128)
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    Book description

    Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.

    Reviews

    'The book is very appealing through its informal style and the variety of topics covered and may be considered the standard reference book in this field.'

    Source: Zentralblatt MATH

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