{"product_id":"zeta-functions-of-graphs-9780521113670","title":"Zeta Functions of Graphs","description":"\u003cp\u003e • Author(s): Audrey Terras\u003cbr\u003e • Publisher: Cambridge University Press\u003cbr\u003e • Publisher Imprint: Cambridge University Press\u003cbr\u003e • BISAC: Discrete Mathematics\u003c\/p\u003e\u003cp\u003eGraph 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.\u003c\/p\u003e","brand":"Cambridge University Press","offers":[{"title":"Hardcover","offer_id":46432840679575,"sku":"9780521113670","price":5331.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780521113670.webp?v=1769306662","url":"https:\/\/atlanticbooks.com\/products\/zeta-functions-of-graphs-9780521113670","provider":"Atlantic Books","version":"1.0","type":"link"}