  Let $I$ and $O$ denote two sets of vertices, where $I\cap O =\emptyset$, $|I|
= n$, $|O| = r$, and $B_u(n,r)$ denote the set of unlabeled graphs whose edges
connect vertices in $I$ and $O$. Recently, it was established
in\cite{atmacaoruc2018} that the following two-sided equality holds,
\begin{equation} \label{mainResult} \displaystyle
\frac{\binom{r+2^{n}-1}{r}}{n!}\, \le\, |B_u(n,r)|\, \le\,
2\frac{\binom{r+2^{n}-1}{r}}{n!},\, n < r.\nonumber \end{equation} and exact
formulas were provided in~\cite{atmaca2017size} for $|B_u(2,r)|$ and
$|B_u(3,r)|.$ In this paper, these results are extended to various families of
labeled bipartite graphs.
