Nordhaus--Gaddum relations for degrees and connectivities under the $δ$-complement
The $δ$-complement $G_δ$ of a graph $G$ complements adjacency within each degree class and preserves adjacency between distinct degree classes. We establish sharp lower and upper additive and product Nordhaus--Gaddum bounds for the minimum degree, maximum degree, vertex connectivity, and edge connectivity of $G$ and $G_δ$. We give explicit constructions attaining all stated sharp bounds.
math.CO↗