On eternal domination and Vizing-type inequalities
We show sharp Vizing-type inequalities for eternal domination. Namely, we prove that for any graphs G and H, (Formula presented.) where (Formula presented.) is the eternal domination function, α is the independence number, and (Formula presented.) 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 (Formula presented.) where (Formula presented.) is the Cartesian product. For the eviction model of eternal domination, we show a sharp upper bound for (Formula presented.).
AKCE International Journal of Graphs and Combinatorics
Digital Object Identifier (DOI)
Driscoll, K., Klostermeyer, W.F., Krop, E., Magnant, C., Taylor, P. (2020) On eternal domination and Vizing-type inequalities. AKCE International Journal of Graphs and Combinatorics, 17(3), 708-712.