Remarks on the outer-independent double Italian domination number

• Autorzy: Volkman Lutz

Identyfikatory

DOI

10.7494/OpMath.2021.41.2.259

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

double Italian domination number; outer-independent double Italian domination number; Nordhaus-Gaddum bound

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 2
• Strony: 259--268
• Opis fizyczny: BIbliogr. 12 poz.

Twórcy

autor

Volkman Lutz

• RWTH Aachen University Lehrstuhl II fur Mathematik 52056 Aachen, Germany

Bibliografia

• [1] F. Azvin, N. Jafari Rad, Bounds on the double Italian domination number of a graph, Discuss. Math. Graph Theory (to appear).
• [2] F. Azvin, N. Jafari Rad, L. Volkmann, Bounds on the outer-independent double Italian domination number, Commun. Comb. Optim. 6 (2021), 123-136.
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Uwagi

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