Abstract
Let G be a graph and let S⊆V(G). The set S is a double outer-independent dominating set of G if |N[v]∩S|≥2 for all v∈V(G), and V(G)∖S is independent. Similarly, S is a 2-outer-independent dominating set, if every vertex from V(G)∖S has at least two neighbors in S and V(G)∖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 complexities and present several bounds for them.
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