By Audrey Terras
Graph idea meets quantity idea during this stimulating e-book. Ihara zeta capabilities of finite graphs are reciprocals of polynomials, occasionally in different variables. Analogies abound with number-theoretic features equivalent to Riemann/Dedekind zeta features. for instance, there's a Riemann speculation (which should be fake) and best quantity theorem for graphs. particular structures of graph coverings use Galois conception to generalize Cayley and Schreier graphs. Then non-isomorphic basic graphs with an analogous zeta are produced, displaying you can't pay attention the form of a graph. The spectra of matrices corresponding to the adjacency and aspect adjacency matrices of a graph are necessary to the plot of this publication, which makes connections with quantum chaos and random matrix thought, plus expander/Ramanujan graphs of curiosity in desktop technology. Pitched at starting graduate scholars, the booklet also will attract researchers. Many well-chosen illustrations and diagrams, and routines all through, theoretical and computer-based.