  We have developed efficient parameterized algorithms for the enumeration
problems of graphs arising in chemistry. In particular, we have focused on the
following problems: enumeration of Kekul\'e structures, computation of Hosoya
index, computation of Merrifield-Simmons index, and computation of graph
entropy based on matchings and independent sets. All these problems are known
to be $\# P$-complete. We have developed FPT algorithms for bounded treewidth
and bounded pathwidth for these problems with a better time complexity than the
known state-of-the-art in the literature. We have also conducted experiments on
the entire PubChem database of chemical compounds and tested our algorithms. We
also provide a comparison with naive baseline algorithms for these problems,
along with a distribution of treewidth for the chemical compounds available in
the PubChem database.
