## Abstract

A subset S of vertices in a graph G is a dominating set if every vertex in V(G) \ S is adjacent to a vertex in S. If the graph G has no isolated vertex, then a semipaired dominating set of G is a dominating set of G with the additional property that the set S can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number γ_{pr 2}(G) is the minimum cardinality of a semipaired dominating set of G. Let G be a maximal outerplanar graph of order n with n_{2} vertices of degree 2. We show that if n≥ 5 , then γpr2(G)≤25n. Further, we show that if n≥ 3 , then γpr2(G)≤13(n+n2). Both bounds are shown to be tight.

Original language | English |
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Pages (from-to) | 911-926 |

Number of pages | 16 |

Journal | Journal of Combinatorial Optimization |

Volume | 38 |

Issue number | 3 |

DOIs | |

Publication status | Published - 15 Oct 2019 |

## Keywords

- Maximal outerplanar graphs
- Paired-domination
- Semipaired domination number

## ASJC Scopus subject areas

- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics