## Abstract

In this paper we introduce a parameter that is squeezed between arguably the two most important domination parameters, namely the domination number and the total domination number. We define a set S of vertices in a graph G with no isolated vertices to be 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, denoted by γt2(G), is the minimum cardinality of a semitotal dominating set of G. We show that if G is a connected graph on n > 4 vertices, then γt2(G) < n/2y and we characterize the trees and graphs of minimum degree 2 achieving this bound.

Original language | English |
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Pages (from-to) | 67-81 |

Number of pages | 15 |

Journal | Utilitas Mathematica |

Volume | 94 |

Publication status | Published - Jul 2014 |

## Keywords

- Domination
- Graph
- Semitotal domination
- Total domination

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics