A sharp upper bound for the number of stable sets in graphs with given number of cut edges

Let GG be a connected and simple graph, and let i(G)i(G) denote the number of stable sets in GG. In this letter, we have presented a sharp upper bound for the i(G)i(G)-value among the set of graphs with kk cut edges for all possible values of kk, and characterized the corresponding extremal graphs as well.