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Opis

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.

Szczegóły książki

Kategoria Książki po angielsku Mathematics & science Mathematics Mathematical foundations

• Pełny tytuł: Zeta Functions of Graphs
• Podtytuł: A Stroll through the Garden
• Autor: Audrey Terras
• Język: Angielski
• Oprawa: Twarda
• Liczba stron: 252
• EAN: 9780521113670
• ISBN: 0521113679
• ID: 04090440
• Wydawca: Cambridge University Press
• Waga: 532 g
• Wymiary: 229 × 157 × 21 mm
• Data wydania: 18. November 2010

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