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Zeta functions of graphs = a stroll ...

Terras, Audrey.

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Zeta functions of graphs = a stroll through the garden /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Zeta functions of graphs/ Audrey Terras.
其他題名:	a stroll through the garden /
作者:	Terras, Audrey.
出版者:	Cambridge :Cambridge University Press, : 2011.,
面頁冊數:	xii, 239 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Graph theory. -
電子資源:	https://doi.org/10.1017/CBO9780511760426
ISBN:	9780511760426

Zeta functions of graphs = a stroll through the garden /
Terras, Audrey.

Zeta functions of graphsa stroll through the garden /[electronic resource] :Audrey Terras. - Cambridge :Cambridge University Press,2011. - xii, 239 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;128. - Cambridge studies in advanced mathematics ;128..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9780511760426Subjects--Topical Terms:

523815
Graph theory.

LC Class. No.: QA166 / .T47 2011

Dewey Class. No.: 511.5

Zeta functions of graphs = a stroll through the garden /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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. 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.
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