Graphs with given number of cut vertices and extremal Merrifield–Simmons index

AbstractThe Merrifield–Simmons index of a graph is defined as the total number of its independent sets, including the empty set. Denote by G(n,k) the set of connected graphs with n vertices and k cut vertices. In this paper, we characterize the graphs with the maximum and minimum Merrifield–Simmons index, respectively, among all graphs in G(n,k) for all possible k values