Tichy, Robert F.; Wagner, Stephan G. Algorithmic generation of molecular graphs with large Merrifield-Simmons index. (English) Zbl 1141.05077 MATCH Commun. Math. Comput. Chem. 59, No. 1, 239-252 (2008). The Merrifield-Simmons index of a graph \(G\) is equal to the number of independent-vertex sets of \(G\). An algorithm for constructing trees with large Merrifield-Simmons index is developed. The algorithm works for so-called ‘acyclic molecular graphs’, that is trees in which the maximal vertex degree does not exceed 4. The structure of such trees having maximal Merrifield-Simmons index is conjectured. Reviewer: Ivan Gutman (Kragujevac) Cited in 2 Documents MSC: 05C85 Graph algorithms (graph-theoretic aspects) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C90 Applications of graph theory 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) Keywords:graph algorithm; chemistry PDFBibTeX XMLCite \textit{R. F. Tichy} and \textit{S. G. Wagner}, MATCH Commun. Math. Comput. Chem. 59, No. 1, 239--252 (2008; Zbl 1141.05077)