Biblioteca Dr. Antonio Monteiro · Catálogo | |
LDR | ·····cam##22·····#a#4500 |
001 | 006694 |
005 | 20121031175525.0 |
008 | 100615s2011####enka#####b####001#0#eng## |
245 | 10 | $a Zeta functions of graphs : $b a stroll through the garden / $c Audrey Terras. |
260 | ## | $a Cambridge ; $a New York : $b Cambridge University Press, $c 2011. |
300 | ## | $a xii, 239 p. : $b il. ; $c 24 cm. |
490 | 0# | $a Cambridge studies in advanced mathematics ; $v 128 |
504 | ## | $a Incluye referencias bibliográficas (p. 230-235) e índice. |
520 | ## | $a "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."-- $c Provided by publisher. |
510 | 4# | $a MR, $c 2012d:05016 |
020 | ## | $a 9780521113670 |
100 | 1# | $a Terras, Audrey. |
650 | #0 | $a Graph theory. |
650 | #0 | $a Functions, Zeta. |
084 | ## | $a 05-02 (05C25 11M41) $2 msc2000 |
010 | ## | $a ##2010024611 |
040 | ## | $a DLC $c DLC $d DLC |
856 | 42 | $3 Publisher description $u http://www.loc.gov/catdir/enhancements/fy1108/2010024611-d.html |
856 | 41 | $3 Table of contents $u http://www.loc.gov/catdir/enhancements/fy1108/2010024611-t.html |
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