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Currently displaying 1 – 3 of 3

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Études sur les machines magnéto-électriques

J. Joubert — 1881

Annales scientifiques de l'École Normale Supérieure

Sur la phosphorescence du phosphore

J. Joubert — 1874

Annales scientifiques de l'École Normale Supérieure

Restrained domination in unicyclic graphs

Johannes H. Hattingh; Ernst J. Joubert; Marc Loizeaux; Andrew R. Plummer; Lucas van der Merwe — 2009

Discussiones Mathematicae Graph Theory

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 $γ_{r} (U) \geq ⎡ n / 3 ⎤$ , and provide a characterization of graphs achieving this bound.

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