Zeta functions of graphs : a stroll through the garden /
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| Author / Creator: | Terras, Audrey. |
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| Imprint: | New York : Cambridge University Press, 2010. |
| Description: | xii, 239 p. ; 24 cm. |
| Language: | English |
| Series: | Cambridge studies in advanced mathematics ; 128 Cambridge studies in advanced mathematics ; 128. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8266513 |
| Summary: | 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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| Physical Description: | xii, 239 p. ; 24 cm. |
| ISBN: | 9780521113670 0521113679 |