  Strongly chordal graphs are a subclass of chordal graphs. The interest in
this subclass stems from the fact that many problems which are NP-complete for
chordal graphs are solvable in polynomial time for this subclass. However, we
are not aware of any algorithm that can generate instances of this class, often
necessary for testing purposes. In this paper, we address this issue. Our
algorithm first generates chordal graphs, using an available algorithm and then
adds enough edges to make it strongly chordal, unless it is already so. The
edge additions are based on a totally balanced matrix characterizations of
strongly chordal graphs.
