Zeta functions of graphs : a stroll through the garden

Audrey Terras.

Cambridge ; New York : Cambridge University Press, 2011.

xii, 239 págs. : ilustraciones ; 24 cm.

Serie: Cambridge studies in advanced mathematics ; 128

ISBN: 9780521113670

Resumen: "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, are included throughout."—Provided by publisher.

Incluye referencias bibliográficas (p. 230-235) e índice.

Reseña: MathSciNet, 2012d:05016