Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON [1, 2]-DOMINATION IN TREES

  • Chen, Xue-Gang (Department of Mathematics North China Electric Power University) ;
  • Sohn, Moo Young (Department of Mathematics Changwon National University)
  • Received : 2017.04.26
  • Accepted : 2017.11.07
  • Published : 2018.04.30
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Abstract

Chellai et al. [3] gave an upper bound on the [1, 2]-domination number of tree and posed an open question "how to classify trees satisfying the sharp bound?". Yang and Wu [5] gave a partial solution for tree of order n with ${\ell}$-leaves such that every non-leaf vertex has degree at least 4. In this paper, we give a new upper bound on the [1, 2]-domination number of tree which extends the result of Yang and Wu. In addition, we design a polynomial time algorithm for solving the open question. By using this algorithm, we give a characterization on the [1, 2]-domination number for trees of order n with ${\ell}$ leaves satisfying $n-{\ell}$. Thereby, the open question posed by Chellai et al. is solved.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

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