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Bounding the total domination subdivision number of a graph in terms of its order

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Abstract

The total domination subdivision number \(\mathrm{sd}_{\gamma _{t}}(G)\) of a graph G is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper we prove that \(\mathrm{sd}_{\gamma_{t}}(G)\leq \lfloor\frac{2n}{3}\rfloor\) for any simple connected graph G of order n≥3 other than K 4. We also determine all simple connected graphs G with \(\mathrm{sd}_{\gamma_{t}}(G)=\lfloor\frac{2n}{3}\rfloor\) .

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Authors and Affiliations

  1. LRI, UMR 8623, Univ. Paris-Sud, Orsay, 91405, France

    Odile Favaron

  2. CNRS, Orsay, 91405, France

    Odile Favaron

  3. Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, IR, Iran

    Hossein Karami & Seyyed Mahmoud Sheikholeslami

Authors
  1. Odile Favaron
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  2. Hossein Karami
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  3. Seyyed Mahmoud Sheikholeslami
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Corresponding author

Correspondence to Seyyed Mahmoud Sheikholeslami.

Additional information

S.M. Sheikholeslami research supported by the Research Office of Azarbaijan University of Tarbiat Moallem.

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Favaron, O., Karami, H. & Sheikholeslami, S.M. Bounding the total domination subdivision number of a graph in terms of its order. J Comb Optim 21, 209–218 (2011). https://doi.org/10.1007/s10878-009-9224-y

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  • DOI: https://doi.org/10.1007/s10878-009-9224-y

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