TY  - BOOK
AU  - Terras,Audrey
TI  - Zeta Functions of Graphs: A Stroll through the Garden 
T2  - Cambridge Studies in Advanced Mathematics
SN  - 9780511760426 (ebook)
AV  - QA166 .T47 2011
U1  - 511/.5 22
PY  - 2010///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Graph theory
KW  - Functions, Zeta
N1  - Title from publisher's bibliographic system (viewed on 04 Apr 2016)
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. 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
UR  - http://dx.doi.org/10.1017/CBO9780511760426
ER  -