On eternal domination and Vizing-type inequalities
Keith Driscoll, William F. Klostermeyer, Elliot Krop and 2 more
AKCE International Journal of Graphs and Combinatorics · 2020
doi:10.1016/j.akcej.2019.12.013 (opens in a new tab)
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Abstract
We show sharp Vizing-type inequalities for eternal domination. Namely, we prove that for any graphs G and H, where is the eternal domination function, α is the independence number, and is the strong product of graphs. This addresses a question of Klostermeyer and Mynhardt. We also show some families of graphs attaining the strict inequality where is the Cartesian product. For the eviction model of eternal domination, we show a sharp upper bound for
Abstract licence: CC BY-NC
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