{"product_id":"9781139635493","title":"Zeta Functions of Graphs: A Stroll through the Garden","description":"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.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":47107922034928,"sku":"9781139635493","price":64.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781139635493_p0.jpg?v=1763700082","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781139635493","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}