Zeta functions from graphs

AKCE International Journal of Graphs and Combinatorics

Simon Davis¹ 

[1] Research Foundation of Southern California8837 Villa La Jolla Drive 13595;

关键词: graph;    zeta function;    adjacency matrix;    eigenvalues;   

DOI  :  10.1016/j.akcej.2017.09.007

来源: DOAJ

【 摘 要 】

The location of the nontrivial poles of a generalized zeta function is derived from the spectrum of Ramanujan graphs and bounds are established for irregular graphs. The existence of a similarity transformation of the diagonal matrix given by a specified set of eigenvalues to an adjacency matrix of a graph is proven, and the method yields a set of finite graphs with eigenvalues determined approximately by a finite subset of the poles of the Ihara zeta function.

【 授权许可】

Unknown