## Abstract

Let G be a graph with no isolated vertex. In this paper, we study a parameter that is squeezed between arguably the two most important dom- ination parameters; namely, the domination number, (G), and the total domination number, Υ(G). A set S of vertices in a graph G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number, Υ2(G), is the minimum cardinality of a semitotal dominating set of G. We observe that (G) ≤ Υ2(G) ≤ Υ(G). We characterize the set of vertices that are contained in all, or in no minimum semitotal dominating set of a tree.

Original language | English |
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Pages (from-to) | 71-93 |

Number of pages | 23 |

Journal | Discussiones Mathematicae - Graph Theory |

Volume | 36 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2016 |

## Keywords

- Domination
- Semitotal domination
- Trees

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics