  In this paper we study Cayley graphs on $\PGL_2(\mathbb F_q)$ mod the
unipotent subgroup, the split and nonsplit tori, respectively. Using the
Kirillov models of the representations of $\PGL_2(\mathbb F_q)$ of degree
greater than one, we obtain explicit eigenvalues of these graphs and the
corresponding eigenfunctions. Character sum estimates are then used to conclude
that two types of the graphs are Ramanujan, while the third is almost
Ramanujan. The graphs arising from the nonsplit torus were previously studied
by Terras et al. We give a different approach here.
