Safe set problem on graphs

@article{Fujita2016SafeSP,
  title={Safe set problem on graphs},
  author={Shinya Fujita and Gary MacGillivray and Tadashi Sakuma},
  journal={Discrete Applied Mathematics},
  year={2016},
  volume={215},
  pages={106-111}
}
A non-empty subset S of the vertices of a connected graph G = ( V ( G ) , E ( G ) ) is a safe set if, for every connected component C of G S and every connected component D of G - S , we have | C | ź | D | whenever there exists an edge of G between C and D . If G S is connected, then S is called a connected safe set. We discuss the minimum sizes of safe sets and connected safe sets in connected graphs. 
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