  In this paper we construct explicit LPS-type Ramanujan graphs from each
definite quaternion algebra over $\mathbb Q$ of class number 1, extending the
constructions of Lubotzky, Phillips, Sarnak, and later Chiu, and answering in
the affirmative a question raised by Jo and Yamasaki. We do this by showing
that for each definite quaternion algebra $\mathcal H$ over $\mathbb Q$ of
class number 1 with maximal order $\mathcal O$, if $G = \mathcal
H^\times/Z(\mathcal H^\times)$ and $p$ is prime such that $G(\mathbb Q_p) \cong
PGL_2(\mathbb Q_p)$, then there exists a congruence $p$-arithmetic subgroup of
$G$ which acts simply transitively on the Bruhat-Tits tree of $G(\mathbb Q_p)$.
