## Abstract

A dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in S, then S is a total dominating set of G. The domination number, γ(G) , and total domination number, γ_{t}(G) , are the minimum cardinalities of a dominating set and total dominating set, respectively, in G. The upper domination number, Γ (G) , and the upper total domination number, Γ _{t}(G) , are the maximum cardinalities of a minimal dominating set and total dominating set, respectively, in G. It is known that γ_{t}(G) / γ(G) ≤ 2 and Γ _{t}(G) / Γ (G) ≤ 2 for all graphs G with no isolated vertex. In this paper we characterize the connected cubic graphs G satisfying γ_{t}(G) / γ(G) = 2 , and we characterize the connected cubic graphs G satisfying Γ _{t}(G) / Γ (G) = 2.

Original language | English |
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Pages (from-to) | 261-276 |

Number of pages | 16 |

Journal | Graphs and Combinatorics |

Volume | 34 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

## Keywords

- Cubic graph
- Domination number
- Total domination number
- Upper domination number
- Upper total domination number

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics