Enumeration of bipartite graphs and bipartite blocks
Andrew Gainer-Dewar, Ira M. Gessel

TL;DR
This paper uses combinatorial species theory to compute the cycle index, enabling the enumeration of unlabeled bipartite graphs and bipartite blocks.
Contribution
It introduces a novel application of combinatorial species to count bipartite structures, providing explicit formulas for unlabeled cases.
Findings
Cycle index for bipartite graphs computed
Enumeration formulas for unlabeled bipartite graphs derived
Counting bipartite blocks achieved
Abstract
Using the theory of combinatorial species, we compute the cycle index for bipartite graphs, which we use to count unlabeled bipartite graphs and bipartite blocks.
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