Abstract:Uses i(G) to denote Merrifield-Simmons index of graph G and defines it as the number of the independent sets of G. Investigates the Merrifield-Simmons index of unicyclic graphs by the technique of graphs transformation on Merrifield-Simmons index, obtains the first eight largest unicyclic graphs with respect to Merrifield-Simmons index, and depicts the extremal graphs.