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Zeta Functions of Graphs : A Stroll Through the Garden
- Publication Year :
- 2011
-
Abstract
- 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.
- Subjects :
- Graph theory
Functions, Zeta
Subjects
Details
- Language :
- English
- ISBNs :
- 9780521113670 and 9780511918681
- Volume :
- 00128
- Database :
- eBook Index
- Journal :
- Zeta Functions of Graphs : A Stroll Through the Garden
- Publication Type :
- eBook
- Accession number :
- 337707