TY  - JOUR
ID  - Volkmann2021
LB  - Volkmann2021
AU  - Volkmann, Lutz
TI  - Remarks on the outer-independent double Italian domination number
ST  - Remarks on the outer-independent double Italian domination number
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 2
SP  - 259
EP  - 268
DO  - https://doi.org/10.7494/OpMath.2021.41.2.259
UR  - https://doi.org/10.7494/OpMath.2021.41.2.259
AB  - 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 \(f:V(G)\longrightarrow \{0,1,2,3\}\) such that if \(f(v)\in\{0,1\}\) for a vertex \(v\in V(G)\), then \(\sum_{x\in N[v]}f(x)\ge 3\), and the set \(\{u\in V(G):f(u)=0\}\) is independent. The weight of an OIDIDF \(f\) is the sum \(\sum_{v\in V(G)}f(v)\). 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, 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.
KW  - double Italian domination number
KW  - outer-independent double Italian domination number
KW  - Nordhaus-Gaddum bound
SN  - 1232-9274
ER  -