Self-complementary (Pseudo-)Split Graphs
Combinatorics
2023-12-19 v1
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.
Cite
@article{arxiv.2312.10413,
title = {Self-complementary (Pseudo-)Split Graphs},
author = {Yixin Cao and Haowei Chen and Shenghua Wang},
journal= {arXiv preprint arXiv:2312.10413},
year = {2023}
}