Opuscula Math. 38, no. 3 (2018), 409-425

Opuscula Mathematica

On domination multisubdivision number of unicyclic graphs

Joanna Raczek

Abstract. The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622-628], we constructively characterize all connected unicyclic graphs with the domination multisubdivision number equal to 3. We end with further questions and open problems.

Keywords: domination number, domination subdivision number, domination multisubdivision number, trees, unicyclic graphs.

Mathematics Subject Classification: 05C69, 05C05, 05C38.

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  • Joanna Raczek
  • Gdansk University of Technology, Department of Technical Physics and Applied Mathematics, Narutowicza 11/12, 80–233 Gdańsk, Poland
  • Communicated by Andrzej Żak.
  • Received: 2017-01-01.
  • Revised: 2017-12-23.
  • Accepted: 2018-01-09.
  • Published online: 2018-03-19.
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Cite this article as:
Joanna Raczek, On domination multisubdivision number of unicyclic graphs, Opuscula Math. 38, no. 3 (2018), 409-425, https://doi.org/10.7494/OpMath.2018.38.3.409

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