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

Abstract

The Merrifield–Simmons index $i\left(G\right)$ 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.