no. 4
Nordhaus–Gaddum type inequalities on the total Italian domination number in graphs
RAIRO. Operations Research, Tome 56 (2022) no. 4, pp. 2235-2243

Let G be a graph with vertex set V(G). A total Italian dominating function (TIDF) on a graph G is a function f : V(G) → {0, 1, 2} such that (i) every vertex v with f(v) = 0 is adjacent to a vertex u with f(u) = 2 or to two vertices w and z with f(w) = f(z) = 1, and (ii) every vertex v with f(v) ≥ 1 is adjacent to a vertex u with f(u) ≥ 1. The total Italian domination number γ$$(G) on a graph G is the minimum weight of a total Italian dominating function. In this paper, we present Nordhaus–Gaddum type inequalities for the total Italian domination number.

DOI : 10.1051/ro/2022108
Keywords: Total domination, total Italian domination number, total Roman domination, 05C69 
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Sheikholeslami, Seyed Mahmoud; Volkmann, Lutz. Nordhaus–Gaddum type inequalities on the total Italian domination number in graphs. RAIRO. Operations Research, Tome 56 (2022) no. 4, pp. 2235-2243. doi: 10.1051/ro/2022108

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