| Zeta Functions of Graphs: A Stroll Through the Garden Contributor(s): Terras, Audrey (Author) |
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ISBN: 0521113679 ISBN-13: 9780521113670 Publisher: Cambridge University Press OUR PRICE: $78.84 Product Type: Hardcover - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Discrete Mathematics - Mathematics | Graphic Methods |
| Dewey: 511.5 |
| LCCN: 2010024611 |
| Series: Cambridge Studies in Advanced Mathematics (Hardcover) |
| Physical Information: 0.6" H x 6.1" W x 9.1" (1.14 lbs) 252 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. 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. |
Contributor Bio(s): Terras, Audrey: - Audrey Terras is Professor of Mathematics at the University of California, San Diego. |