Zeta functions of graphs : a stroll through the garden / Audrey Terras.
"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 (whic...
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Main Author: | |
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Language: | English |
Published: |
Cambridge, UK ; New York :
Cambridge University Press,
2011.
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Series: | Cambridge studies in advanced mathematics ;
128. |
Subjects: | |
Local Note: |
This resource was acquired with funds from Office of the Provost, Michigan State University, in honor of Professor Edgar M. Palmer, who retired from the Department of Mathematics in 2011. |
Physical Description: | xii, 239 pages : illustrations (some color) ; 24 cm. |
Format: | Book |
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. 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"--Provided by publisher. |
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Call Number: | QA166 .T47 2011 |
Bibliography Note: | Includes bibliographical references and index. |
ISBN: | 9780521113670 (hardback) 0521113679 (hardback) |