The Hosoya indices and Merrifield–Simmons indices of graphs with connectivity at most

The Hosoya index and the Merrifield–Simmons index of a graph are defined as the total number of the matchings (including the empty edge set) and the total number of the independent vertex sets (including the empty vertex set) of the graph, respectively. Let V n , k be the set of connected n -vertex graphs with connectivity at most k . In this note, we characterize the extremal (maximal and minimal) graphs from V n , k with respect to the Hosoya index and the Merrifield–Simmons index, respectively.