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arXiv · 1812.10946

On three outer-independent domination related parameters in graphs

Doost Ali Mojdeh·Iztok Peterin·Babak Samadi·Ismael G. Yero
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Abstract

Let $G$ be a graph and let $S\subseteq V(G)$. The set $S$ is a double outer-independent dominating set of $G$ if $|N[v]\cap D|\geq2$, for all $v\in V(G)$, and $V(G)\setminus S$ is independent. Similarly, $S$ is a $2$-outer-independent dominating set, if every vertex from $V(G)\setminus S$ has at least two neighbors in $S$ and $V(G)\setminus S$ is independent. Finally, $S$ is a total outer-independent dominating set if every vertex from $V(G)$ has a neighbor in $S$ and the complement of $S$ is an independent set. The double, total or $2$-outer-independent domination number of $G$ is the smallest possible cardinality of any double, total or $2$-outer-independent dominating set of $G$, respectively. In this paper, the $2$-outer-independent, the total outer-independent and the double outer-independent domination numbers of graphs are investigated. We prove some Nordhaus-Gaddum type inequalities, derive their computational complexity and present several bounds for them.

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Doost Ali Mojdeh, Iztok Peterin, Babak Samadi, Ismael G. Yero. 2018-12-28. On three outer-independent domination related parameters in graphs. https://doi.org/10.1016/j.dam.2021.01.027

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