Doubly connected domination in the corona and lexicographic product of graphs

@article{Arriola2014DoublyCD,
  title={Doubly connected domination in the corona and lexicographic product of graphs},
  author={Benjier H. Arriola and S. Canoy},
  journal={Applied mathematical sciences},
  year={2014},
  volume={8},
  pages={1521-1533}
}
Let G be a simple connected graph. A connected dominating set S ⊆ V (G) is called a doubly connected dominating set of G if the subgraph 〈V (G)\S〉 induced by V (G)\S is connected. In this paper, we show that any three positive integers a, b, and c with 4 ≤ a ≤ b ≤ c, where b ≤ 2a− 3 if a is odd and b ≤ 2a− 2 if a is even, are realizable as the total domination, connected domination, and doubly connected domination numbers. Also, we characterize the doubly connected dominating sets in the corona… Expand
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