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 Gröbner 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 \(R_\Delta\) .
