Algorithmic aspects of upper paired-domination in graphs

Michael A. Henning, D. Pradhan

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


A set D of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to a vertex in D and the subgraph induced by D contains a perfect matching (not necessarily as an induced subgraph). A paired-dominating set of G is minimal if no proper subset of it is a paired-dominating set of G. The upper paired-domination number of G, denoted by Γpr(G), is the maximum cardinality of a minimal paired-dominating set of G. In UPPER-PDS, it is required to compute a minimal paired-dominating set with cardinality Γpr(G) for a given graph G. In this paper, we show that UPPER-PDS cannot be approximated within a factor of n1−ε for any ε>0, unless P=NP and UPPER-PDS is APX-complete for bipartite graphs of maximum degree 4. On the positive side, we show that UPPER-PDS can be approximated within O(Δ)-factor for graphs with maximum degree Δ. We also show that UPPER-PDS is solvable in polynomial time for threshold graphs, chain graphs, and proper interval graphs.

Original languageEnglish
Pages (from-to)98-114
Number of pages17
JournalTheoretical Computer Science
Publication statusPublished - 12 Jan 2020


  • APX-complete
  • Domination
  • NP-complete
  • Paired-domination
  • Polynomial time algorithm
  • Upper paired-domination

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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