Abstract:The $\delta$-complement $G_\delta$ 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 $G_\delta$. We give explicit constructions attaining all stated sharp bounds.
From: Panupong Vichitkunakorn [view email]
[v1]
Sun, 4 Feb 2024 14:42:37 UTC (8 KB)
[v2]
Thu, 4 Jun 2026 09:15:05 UTC (8 KB)
[v3]
Thu, 17 Sep 2026 16:09:55 UTC (13 KB)
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