The Merrifield–Simmons index \({\sigma(G)}\) of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are non-adjacent, i.e., the number of independent-vertex sets of G. By T(n,k) we denote the set of trees with n vertices and with k pendent vertices. In this paper, we investigate the Merrifield–Simmons index \({\sigma(T)}\) for a tree T in T(n,k). For all trees in T(n,k), we determined unique trees with the first and second largest Merrifield–Simmons index, respectively.
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Wang, M., Hua, H. & Wang, D. The first and second largest Merrifield–Simmons indices of trees with prescribed pendent vertices. J Math Chem 43, 727–736 (2008). https://doi.org/10.1007/s10910-006-9224-4
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DOI: https://doi.org/10.1007/s10910-006-9224-4