Abstract
We present an algorithm to test whether a given graphical degree sequence is forcibly biconnected. The worst case time complexity of the algorithm is shown to be exponential but it is still much better than the previous basic algorithm for this problem. We show through experimental evaluations that the algorithm is efficient on average. We also adapt the classic algorithm of Ruskey et al. and that of Barnes and Savage to 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 $C$ ($0
Highlights
We consider graphical degree sequences of finite simple graphs where the order of the terms in the sequence does not matter
We present an algorithm to test whether a given graphical degree sequence is forcibly biconnected
We adapt the classic algorithm of Ruskey et al and that of Barnes and Savage to obtain some enumerative results about forcibly biconnected graphical degree sequences of given length n and forcibly biconnected graphical partitions of given even integer n
Summary
We consider graphical degree sequences of finite simple graphs (i.e. finite undirected graphs without loops or multiple edges) where the order of the terms in the sequence does not matter. Based on these enumerative results we make some conjectures about the relative asymptotic behavior of considered functions and the unimodality of certain associated integer sequences.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
