Secure weakly connected domination in the join of graphs

@article{Leonida2015SecureWC,
  title={Secure weakly connected domination in the join of graphs},
  author={Rene E. Leonida and Rendon A. Dela Cruz and Emmylou M. Aujero and Marchelle A. Deleverio and Nimfa L. Bodegas},
  journal={International Journal of Mathematical Analysis},
  year={2015},
  volume={9},
  pages={259-263}
}
  • Rene E. Leonida, Rendon A. Dela Cruz, +2 authors Nimfa L. Bodegas
  • Published 2015
  • Computer Science
  • International Journal of Mathematical Analysis
  • In this paper, we take a look at the secure weakly connected domination in the join of graphs. In particular, we obtain the bounds for the secure weakly connected domination number of the join and, give necessary and sufficient conditions for the join to have secure weakly connected domination number equal to 1, 2 and 3. Mathematics Subject Classification: 05C69 

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    Also, D 1 = {u, v} is a weakly connected dominating set of N G+H [D 1 ]. Thus, (S\{w}) ∪ {z} = {u, v, z} is a weakly connected dominating set of G + H
    • Also, D 1 = {u, v} is a weakly connected dominating set of N G+H [D 1 ]. Thus, (S\{w}) ∪ {z} = {u, v, z} is a weakly connected dominating set of G + H
    Hence, S is a secure weakly connected dominating set of
    • Hence, S is a secure weakly connected dominating set of
    Remark 2.6 Let m ≥ 4 and n ≥ 4 be integers. Then γ sw
    • Remark 2.6 Let m ≥ 4 and n ≥ 4 be integers. Then γ sw