| Record ID | marc_loc_2016/BooksAll.2016.part37.utf8:141052723:2240 |
| Source | Library of Congress |
| Download Link | /show-records/marc_loc_2016/BooksAll.2016.part37.utf8:141052723:2240?format=raw |
LEADER: 02240cam a2200301 a 4500
001 2010024611
003 DLC
005 20110421084734.0
008 100615s2011 enka b 001 0 eng
010 $a 2010024611
020 $a9780521113670
040 $aDLC$cDLC$dDLC
042 $apcc
050 00 $aQA166$b.T47 2011
082 00 $a511/.5$222
100 1 $aTerras, Audrey.
245 10 $aZeta functions of graphs :$ba stroll through the garden /$cAudrey Terras.
260 $aCambridge ;$aNew York :$bCambridge University Press,$c2011.
300 $axii, 239 p. :$bill. ;$c24 cm.
490 0 $aCambridge studies in advanced mathematics ;$v128
504 $aIncludes bibliographical references (p. 230-235) and index.
520 $a"Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Pitched at beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and diagrams, and exercises throughout, theoretical and computer-based"--$cProvided by publisher.
650 0 $aGraph theory.
650 0 $aFunctions, Zeta.
856 42 $3Cover image$uhttp://assets.cambridge.org/97805211/13670/cover/9780521113670.jpg
856 42 $3Contributor biographical information$uhttp://www.loc.gov/catdir/enhancements/fy1108/2010024611-b.html
856 42 $3Publisher description$uhttp://www.loc.gov/catdir/enhancements/fy1108/2010024611-d.html
856 41 $3Table of contents only$uhttp://www.loc.gov/catdir/enhancements/fy1108/2010024611-t.html