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On the total domination subdivision number in some classes of graphs

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Abstract

A set S of vertices of a graph G=(V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number \(\mathrm {sd}_{\gamma_{t}}(G)\) 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 \(\mathrm {sd}_{\gamma_{t}}(G)\leq\gamma_{t}(G)+1\) for some classes of graphs.

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Authors and Affiliations

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

    O. Favaron

  2. Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran

    H. Karami, R. Khoeilar & S. M. Sheikholeslami

Authors
  1. O. Favaron
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  2. H. Karami
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  3. R. Khoeilar
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  4. S. M. Sheikholeslami
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Corresponding author

Correspondence to S. M. Sheikholeslami.

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Favaron, O., Karami, H., Khoeilar, R. et al. On the total domination subdivision number in some classes of graphs. J Comb Optim 20, 76–84 (2010). https://doi.org/10.1007/s10878-008-9193-6

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  • DOI: https://doi.org/10.1007/s10878-008-9193-6

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