%0 Journal Article %A M. S. Haghighat and A. Dolati and M. Tabari and E. Mohseni %D 2010 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 45, 2010 %T The Extremal Graph with the Largest Merrifield-Simmons Index of (n, n + 2)-graphs %U https://publications.waset.org/pdf/14643 %V 45 %X The Merrifield-Simmons index of a graph G is defined as the total number of its independent sets. A (n, n + 2)-graph is a connected simple graph with n vertices and n + 2 edges. In this paper we characterize the (n, n+2)-graph with the largest Merrifield- Simmons index. We show that its Merrifield-Simmons index i.e. the upper bound of the Merrifield-Simmons index of the (n, n+2)-graphs is 9 × 2n-5 +1 for n ≥ 5. %P 1339 - 1341