  The idea of graph compositions, which was introduced by A. Knopfmacher and M.
E. Mays, generalizes both ordinary compositions of positive integers and
partitions of finite sets. In their original paper they developed formulas,
generating functions, and recurrence relations for composition counting
functions for several families of graphs. Here we show that some of the results
involving compositions of bipartite graphs can be derived more easily using
exponential generating functions.
