Self-complementary (Pseudo-)Split Graphs

We study split graphs and pseudo-split graphs that are isomorphic to their complements. These special subclasses of self-complementary graphs are actually the core of self-complementary graphs. Indeed, we show that all realizations of 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.