  We are concerned with split graphs and pseudo-split graphs whose complements
are isomorphic to themselves. These special subclasses of self-complementary
graphs are actually the core of self-complementary graphs. Indeed, we show that
all self-complementary graphs with forcibly self-complementary degree sequences
are pseudo-split graphs. We also give formulas to calculate the number of
self-complementary (pseudo-)split graphs of a given order, and show that
Trotignon's conjecture holds for all self-complementary split graphs.
