The smallest Merrifield–Simmons index of (n,n+1)(n,n+1)-graphs

The Merrifield–Simmons index of a graph is defined as the total number of its independent sets. In this paper, we show that the smallest Merrifield–Simmons index of (n,n+1)(n,n+1)-graphs is f(n)+2f(n−2)+f(n−4)f(n)+2f(n−2)+f(n−4), where f(n)f(n) is the nnth Fibonacci number, and characterize the extremal graphs.