- Tytuł:
- Remarks on the outer-independent double Italian domination number
- Autorzy:
- Volkman, Lutz
- Powiązania:
- https://bibliotekanauki.pl/articles/2051048.pdf
- Data publikacji:
- 2021
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
double Italian domination number
outer-independent double Italian domination number
Nordhaus-Gaddum bound - Opis:
- Let $G$ be a graph with vertex set $V(G)$. If $u \in V(G)$, then $N[u]$ is the closed neighborhood of $u$. An outer-independent double Italian dominating function (OIDIDF) on a graph $G$ is a function $ƒ : V(G) \rightarrow \{0, 1, 2, 3\}$ such that if $ƒ (v) \in \{0, 1\}$ for a vertex $v \in V(G)$, then $\Sigma_{x \in N[v]} f(x) \geq 3$, and the set ${u \in V(G) : f (u) = 0}$ is independent. The weight of an OIDIDF $f$ is the sum $\Sigma_{v \in V(G)} f(v)$. The outer-independent double Italian domination number $\gamma_{oidI}(G)$ 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, \textit{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.
- Źródło:
-
Opuscula Mathematica; 2021, 41, 2; 259-268
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł