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[DOWNLOAD] "Zeta Functions of Graphs" by Audrey Terras " eBook PDF Kindle ePub Free

Zeta Functions of Graphs

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eBook details

  • Title: Zeta Functions of Graphs
  • Author : Audrey Terras
  • Release Date : January 18, 2010
  • Genre: Mathematics,Books,Science & Nature,
  • Pages : * pages
  • Size : 15845 KB

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.


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