Compositions of graphs revisited (Q1010587)

Summary: The idea of graph compositions, which was introduced by \textit{A. Knopfmacher} and \textit{M. E. Mays} [Integers 1, Paper A04, 11 p., electronic only (2001; Zbl 0979.05062)], 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.