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Zeta Functions of Graphs by Audrey Terras

Zeta Functions of Graphs

by Audrey Terras
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Book cover type: Hardcover
  • ISBN13: 9780521113670
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date: N/A
  • Pages: 252
  • Original Price: GBP 66.0
  • Language: English
  • Edition: N/A
  • Item Weight: 518 grams
  • BISAC Subject(s): Discrete Mathematics

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. Pitched at beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and diagrams, and exercises throughout, theoretical and computer-based.

Terras, Audrey: - Audrey Terras is Professor of Mathematics at the University of California, San Diego.

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