The optimal average information ratio of secret-sharing schemes for the access structures based on unicycle graphs and bipartite graphs

In this paper, we derive bounds on the optimal average information ratio of the access structures based on general graphs and investigate the value of the ratio for unicycle graphs and some bipartite graphs. We determine the exact values of this ratio for some infinite classes of bipartite graphs and unicycle graphs. This extends previous results. We also provide good bounds on the optimal average information ratio for all unicycle graphs.