Secure convex domination in a graph

@article{Enriquez2015SecureCD,
  title={Secure convex domination in a graph},
  author={E. L. Enriquez and S. Canoy},
  journal={International Journal of Mathematical Analysis},
  year={2015},
  volume={9},
  pages={317-325}
}
In this paper, we give necessary and sufficient conditions for a subset S of the vertex set of a connected graph G to be a secure convex dominating set. Some realization problems will be given. In particular, we show that given positive integers k and n such that n ≥ 4 and 1 ≤ k ≤ n, there exists a connected graph G with |V (G)| = n and γscon(G) = k. Also, we show that for any positive integers k, m and n such that 1 ≤ k ≤ m− 2 and m ≤ n, there exists a connected graph G with |V (G)| = n, γscon… Expand
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References

SHOWING 1-5 OF 5 REFERENCES
Convex Sets Under Some Graph Operations
  • 35
Convex domination in the composition and cartesian product of graphs
  • 11
  • PDF
Weakly convex and convex domination numbers
  • 36
  • PDF
Convex sets in graphs
  • 77
Convexity , Geodetic , and Hull Numbers of the Join of Graphs
  • Utilitas Mathematica