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arXiv · 2402.02507

Nordhaus--Gaddum relations for degrees and connectivities under the $δ$-complement

Supakorn Srisawat·Panupong Vichitkunakorn
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Abstract

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.

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Supakorn Srisawat, Panupong Vichitkunakorn. 2026-09-17. Nordhaus--Gaddum relations for degrees and connectivities under the $δ$-complement. https://arxiv.org/abs/2402.02507

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