On conjecture of Merrifield–Simmons index

Abstract The total number of independent subsets, including the empty set, of a graph, is also termed as the Merrifield–Simmons index ( M S I ) in mathematical chemistry. The eccentric complexity of a graph G is defined to be the number of different eccentricities of its vertices. Hua et al. (2020) mentioned two open problems and a conjecture on the Merrifield–Simmons index and eccentric complexity of graph. In this paper we solve both open problems and a conjecture. Moreover, we generalize some of the results.