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An Upper Bound for the Total Domination Subdivision Number of a Graph

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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 \({{\rm sd}_{\gamma_t}(G)}\) 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 \({{\rm sd}_{\gamma_t}(G)\leq 2\gamma_t(G)-1}\) for every simple connected graph G of order n ≥ 3.

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Authors and Affiliations

  1. Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, Islamic Republic of Iran

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

  2. Department of Mathematics, University of West Georgia, Carrollton, GA, 30118, USA

    A. Khodkar

Authors
  1. H. Karami
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  2. R. Khoeilar
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  3. S. M. Sheikholeslami
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  4. A. Khodkar
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Corresponding author

Correspondence to S. M. Sheikholeslami.

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Karami, H., Khoeilar, R., Sheikholeslami, S.M. et al. An Upper Bound for the Total Domination Subdivision Number of a Graph. Graphs and Combinatorics 25, 727–733 (2009). https://doi.org/10.1007/s00373-010-0877-1

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  • DOI: https://doi.org/10.1007/s00373-010-0877-1

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