Enumeration of bipartite graphs and bipartite blocks

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.