The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four

The Merrifield–Simmons index i G of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, i.e., the number of independent vertex sets of G . In this paper, we determine the minimum Merrifield–Simmons index of unicyclic graphs with n vertices and diameter at most four.