Graphs with given number of cut vertices and extremal MerrifieldSimmons index ?
The MerrifieldSimmons index of a graph is defined as the total number of its independent sets, including the empty set. Denote by G(n,k) G ( n , k ) the set of connected graphs with n n vertices and k k cut vertices. In this paper, we characterize the graphs with the maximum and minimum MerrifieldSimmons index, respectively, among all graphs in G(n,k) G ( n , k ) for all possible k k values.
merrifieldsimmons index independent sets cut vertex bound extremal graph