  We present an algorithm to test whether a given graphical degree sequence is
forcibly biconnected or not and prove its correctness. The worst case run time
complexity of the algorithm is shown to be exponential but still much better
than the previous basic algorithm presented in \cite{Wang2018}. We show through
experimental evaluations that the algorithm is efficient on average. We also
adapt Ruskey et al's classic algorithm to enumerate zero-free graphical degree
sequences of length $n$ and Barnes and Savage's classic algorithm to enumerate
graphical partitions of an even integer $n$ by incorporating our testing
algorithm into theirs and then obtain some enumerative results about forcibly
biconnected graphical degree sequences of given length $n$ and forcibly
biconnected graphical partitions of given even integer $n$. Based on these
enumerative results we make some conjectures such as: when $n$ is large, (1)
the proportion of forcibly biconnected graphical degree sequences of length $n$
among all zero-free graphical degree sequences of length $n$ is asymptotically
a constant between 0 and 1; (2) the proportion of forcibly biconnected
graphical partitions of even $n$ among all forcibly connected graphical
partitions of $n$ is asymptotically 0.
