  We consider standard graded toric rings $R_{\Delta}$ whose generators
correspond to the faces of a simplicial complex $\Delta$. When $R_{\Delta}$ is
normal, it is shown that its divisor class group is free. For a flag complex
$\Delta$ which is the clique complex of a perfect graph, a nice description for
the class group and the canonical module of $R_{\Delta}$ in terms of the
minimal vertex covers of the graph is given. Moreover, for a quasi-forest
simplicial complex a quadratic Gr\"obner basis for the defining ideal of
$R_{\Delta}$ is presented. Using this fact we give combinatorial descriptions
for the $a$-invariant and the Gorenstein property of $R_\Delta$.
