Total outer-connected domination in trees

@article{Cyman2010TotalOD,
  title={Total outer-connected domination in trees},
  author={Joanna Cyman},
  journal={Discuss. Math. Graph Theory},
  year={2010},
  volume={30},
  pages={377-383}
}
  • Joanna Cyman
  • Published 2010
  • Mathematics
  • Discuss. Math. Graph Theory
Let G = (V, E) be a graph. Set D ⊆ V (G) is a total outerconnected dominating set of G if D is a total dominating set in G and G[V (G)−D] is connected. The total outer-connected domination number of G, denoted by γtc(G), is the smallest cardinality of a total outer-connected dominating set of G. We show that if T is a tree of order n, then γtc(T ) ≥ d 2n 3 e. Moreover, we constructively characterize the family of extremal trees T of order n achieving this lower bound. 

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