Algorithmic generation of molecular graphs with large Merrifield-Simmons index

The Merrifield-Simmons index is related to several physicochemical characteristics and is thus of use in combinatorial chemistry, e.g. in drug design and molecular recognitions. In this paper, we show how one can algorithmically construct databases of acyclic molecular graphs with large Merrifield-Simmons index. Our algorithm can deal with a large number of atoms (several hundreds) in short time by means of an elaborate reduction process, and its results lead to a general conjecture on the structure of acyclic molecular graphs with maximal Merrifield-Simmons index. Finally, we show that the algorithm can be modified to deal with another popular index, the Hosoya index.