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Bounds on the paired domination number of graphs with minimum degree at least three

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  • Henning, Michael A.
  • Pilśniak, Monika
  • Tumidajewicz, Elżbieta

Abstract

A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph). The minimum cardinality of a paired dominating set of G is the paired domination number γpr(G) of G. In this paper, we show that if G is a graph of order n and δ(G)≥3, then γpr(G)≤1903730000n<0.634567n.

Suggested Citation

  • Henning, Michael A. & Pilśniak, Monika & Tumidajewicz, Elżbieta, 2022. "Bounds on the paired domination number of graphs with minimum degree at least three," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    • Handle: RePEc:eee:apmaco:v:417:y:2022:i:c:s009630032100864x
    DOI: 10.1016/j.amc.2021.126782
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    References listed on IDEAS

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    1. Michael A. Henning, 2007. "Graphs with large paired-domination number," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 61-78, January.
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    Cited by:

    1. Annamalai Meenakshi & Adhimoolam Kannan & Robert Cep & Muniyandy Elangovan, 2023. "Efficient Graph Network Using Total Magic Labeling and Its Applications," Mathematics, MDPI, vol. 11(19), pages 1-21, September.

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    More about this item

    Keywords

    Paired domination; Bounds;

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