## Abstract

A dominating set D of a graph G without isolated vertices is called semipaired dominating set if D can be partitioned into 2-element subsets such that the vertices in each set are at distance at most 2. The semipaired domination number, denoted by γpr2(G) is the minimum cardinality of a semipaired dominating set of G. Given a graph G with no isolated vertices, the MINIMUM SEMIPAIRED DOMINATION problem is to find a semipaired dominating set of G of cardinality γpr2(G). The decision version of the MINIMUM SEMIPAIRED DOMINATION problem is already known to be NP-complete for chordal graphs, an important graph class. In this paper, we show that the decision version of the MINIMUM SEMIPAIRED DOMINATION problem remains NP-complete for split graphs, a subclass of chordal graphs. On the positive side, we propose a linear-time algorithm to compute a minimum cardinality semipaired dominating set of block graphs. In addition, we prove that the MINIMUM SEMIPAIRED DOMINATION problem is APX-complete for graphs with maximum degree 3.

Original language | English |
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Article number | 19 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Volume | 23 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2021 |

## Keywords

- Block graphs
- Domination
- Graph algorithms
- NP-completeness
- Semipaired domination

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science
- Discrete Mathematics and Combinatorics