The ext re mal graph with the largest Merrifield - Simmons index of ( n , n + 2 ) - graphs
نویسنده
چکیده
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 MerrifieldSimmons 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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