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

Michael A. Henning, Monika Pilśniak and Elżbieta Tumidajewicz

Applied Mathematics and Computation, 2022, vol. 417, issue C

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.

Keywords: Paired domination; Bounds (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:417:y:2022:i:c:s009630032100864x

DOI: 10.1016/j.amc.2021.126782

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