Geodesic
Generalized connected domination in graphs
Discrete mathematics & theoretical computer science, Tome 8 (2006).

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As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ _c^k (G) of such a smallest set we relate to γ _c(G), the order of a smallest connected dominating set. For a tree T we give bounds on γ _c^k (T) in terms of minimum valency and diameter. For trees the inequality γ _c^k (T)≤ n-k-1 is known to hold, we determine the class of trees, for which equality holds. 
@article{DMTCS_2006_8_a14,
     author = {Kouider, Mekkia and Vestergaard, Preben Dahl},
     title = {Generalized connected domination in graphs},
     journal = {Discrete mathematics & theoretical computer science},
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     year = {2006},
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Kouider, Mekkia; Vestergaard, Preben Dahl. Generalized connected domination in graphs. Discrete mathematics & theoretical computer science, Tome 8 (2006). doi : 10.46298/dmtcs.373. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.373/

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