{"product_id":"zeta-functions-of-graphs","title":"Zeta Functions of Graphs","description":"\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. 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.\u003c\/p\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46646759784686,"sku":"9780521113670","price":106.47,"currency_code":"AUD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0630\/9612\/7726\/files\/9780521113670.jpg?v=1750160691","url":"https:\/\/bookland.com.au\/products\/zeta-functions-of-graphs","provider":"Book Land AU","version":"1.0","type":"link"}