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Bounds on the outer-independent double Italian domination number | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 10، دوره 6، شماره 1، شهریور 2021، صفحه 123-136 اصل مقاله (409.88 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2020.26928.1166 | ||
| نویسندگان | ||
| Farzaneh Azvin1؛ Nader Jafari Rad* 1؛ Lutz Volkmann2 | ||
| 1Shahed University | ||
| 2RWTH Aachen University | ||
| چکیده | ||
| An outer-independent double Italian dominating function (OIDIDF) on a graph $G$ with vertex set $V(G)$ 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 $\sum_{u\in N[v]}f(u)\geq3$, and the set $ \{u\in V(G)|f(u)=0\}$ is independent. The weight of an OIDIDF $f$ is the value $w(f)=\sum_{v\in V(G)}f(v)$. The minimum weight of an OIDIDF on a graph $G$ is called the outer-independent double Italian domination number $\gamma_{oidI}(G)$ of $G$. We present sharp lower bounds for the outer-independent double Italian domination number of a tree in terms of diameter, vertex covering number and the order of the tree. | ||
| کلیدواژهها | ||
| Roman domination؛ outer-independent double Italian domination؛ tree | ||
| مراجع | ||
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