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Paired-Domination Subdivision Numbers of Graphs

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Abstract

A paired-dominating set of a graph G = (V, E) with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by γ pr (G), is the minimum cardinality of a paired-dominating set of G. The paired-domination subdivision number sd γpr (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 paired-domination number. In this paper we establish upper bounds on the paired-domination subdivision number and pose some problems and conjectures.

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Authors and Affiliations

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

    O. Favaron

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

    H. Karami & S. M. Sheikholeslami

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

Correspondence to S. M. 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. Paired-Domination Subdivision Numbers of Graphs. Graphs and Combinatorics 25, 503–512 (2009). https://doi.org/10.1007/s00373-005-0871-1

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  • DOI: https://doi.org/10.1007/s00373-005-0871-1

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