000			01654 a2200217 4500
999			_c54549 _d54549
008			210324b ||||| |||| 00| 0 eng d
020			_a9780521113670
082			_a511.5 _bTER
100			_aTerras, Audrey
245			_aZeta functions of graphs: a stroll through the garden
260			_bCambridge University Press, _c2010. _aCambridge:
300			_axii, 239 p. : ill. ; _bhb, _c23 cm.
365			_aGBP _b52.00
504			_aIncludes bibliographical references (p. 230-235) and index.
520			_aGraph 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.
650			_aZeta Functions
650			_aGraph theory
650			_aComputer algorithms
650			_aTopology
942			_2ddc _cTD