1. Self-complementary (Pseudo-)Split Graphs
- Author
-
Cao, Yixin, Chen, Haowei, and Wang, Shenghua
- Subjects
Mathematics - Combinatorics ,05C07, 05C30 (Primary) 05C60 (Secondary) - Abstract
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.
- Published
- 2023