TY  - GEN
AU  - Terras, Audrey
TI  - Zeta functions of graphs: a stroll through the garden 
SN  - 9780521113670
U1  - 511.5 
PY  - 2010///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Zeta Functions
KW  - Graph theory
KW  - Computer algorithms
KW  - Topology
N1  - Includes bibliographical references (p. 230-235) and index
N2  - 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
ER  -