Remarks on the outer-independent double Italian domination number

Let G be a graph with vertex set V(G). If u ∈ V(G), then N[u] is the closed neighborhood of u. An outer-independent double Italian dominating function (OIDIDF) on a graph G is a function ƒ : V(G) —> {0, 1, 2, 3} such that if ƒ (v) ∈ {0, 1} for a vertex v ∈ V(G), then [formula], and the set {u ∈ V(G) : ƒ (u) = 0} is independent. The weight of an OIDIDF ƒ is the sum [formula]. The outer-independent double Italian domination number [formula] equals the minimum weight of an OIDIDF on G. In this paper we present Nordhaus-Gaddum type bounds on the outer-independent double Italian domination number which improved corresponding results given in [F. Azvin, N. Jafari Rad, L. Volkmann, Bounds on the outer-independent double Italian domination number, Commun. Comb. Optim. 6 (2021), 123-136]. Furthermore, we determine the outer-independent double Italian domination number of some families of graphs.

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).