Ihara zeta function, coefficients of Maclaurin series, and Ramanujan graphs

Hau-Wen Huang

Let $X$ denote a connected $(q+1)$-regular undirected graph of finite order $n$. The graph $X$ is called Ramanujan whenever $$|\lambda |\le 2q^{\frac{1}{2}}$$ for all nontrivial eigenv…