  We introduce a new problem, CSPLib problem number 50, to generate all degree
sequences that have a corresponding diamond-free graph with secondary
properties. This problem arises naturally from a problem in mathematics to do
with balanced incomplete block designs; we devote a section of this paper to
this. The problem itself is challenging with respect to computational effort
arising from the large number of symmetries within the models. We introduce two
models for this problem. The second model is an improvement on the first, and
this improvement largely consists of breaking the problem into two stages, the
first stage producing graphical degree sequences that satisfy arithmetic
constraints and the second part testing that there exists a graph with that
degree sequence that is diamond-free.
