## Abstract

Let (Formula presented.) be a graph. A set (Formula presented.) is a restrained dominating set if every vertex in (Formula presented.) is adjacent to a vertex in (Formula presented.) and to a vertex in (Formula presented.). The restrained domination number of (Formula presented.) , denoted (Formula presented.) , is the smallest cardinality of a restrained dominating set of (Formula presented.). The best possible upper bound (Formula presented.) is established in Joubert (Discrete Appl Math 161:829–837, 2013) on the size (Formula presented.) of a graph (Formula presented.) with a given order (Formula presented.) and restrained domination number (Formula presented.). We extend this result to include the cases (Formula presented.) , and characterize graphs (Formula presented.) of order (Formula presented.) and restrained domination number (Formula presented.) for which (Formula presented.).

Original language | English |
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Pages (from-to) | 1586-1608 |

Number of pages | 23 |

Journal | Journal of Combinatorial Optimization |

Volume | 31 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 May 2016 |

## Keywords

- Domination
- Graph
- Order
- Restrained domination
- Size

## ASJC Scopus subject areas

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