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The Extremal Graph with the Largest Merrifield-Simmons Index of (n, n + 2)-graphs

Authors: M. S. Haghighat, A. Dolati, M. Tabari, E. Mohseni


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.

Keywords: Merrifield-Simmons index, (n, n+2)-graph.

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