2023/12/16 by Cao, Yixin, Chen, Haowei, Wang, Shenghua
#05C07 #05C30 (Primary) 05C60 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2312.10413
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.