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Formally, given an integer $k \\le \\Delta(G)$, a set of vertices $D \\subseteq V(G)$ is called a $k$-limited dominating set if it is a dominating set and, in addition, each vertex of $D$ has at most $k$ neighbors outside $D$. The minimum cardinality of such a set is the $k$-limited domination number, denoted by $\\gamma_k^{\\mathrm{L}}(G)$. 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