Geodesic
Restrained domination in unicyclic graphs
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 1, pp. 71-86.

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Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S. The restrained domination number of G, denoted by γ_r(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then γ_r(U) ≥ ⎡n/3⎤, and provide a characterization of graphs achieving this bound.
Keywords: restrained domination, unicyclic graph 
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Hattingh, Johannes; Joubert, Ernst; Loizeaux, Marc; Plummer, Andrew; van der Merwe, Lucas. Restrained domination in unicyclic graphs. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 1, pp. 71-86. http://geodesic.mathdoc.fr/item/DMGT_2009_29_1_a4/

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