## Abstract

A set S of vertices in a graph G is a total dominating set of G if every vertex has a neighbor in S. The total domination number, γ _{t} (G), is the minimum cardinality of a total dominating set of G. A total forcing set in a graph G is a forcing set (zero forcing set) in G which induces a subgraph without isolated vertices. The total forcing number of G, denoted F _{t} (G), is the minimum cardinality of a total forcing set in G. Our main contribution is to show that the total forcing number and the total domination number of a cubic graph are related. More precisely, we prove that if G is a connected cubic graph different from K _{3,3} , then F _{t} (G)≤[Formula presented]γ _{t} (G).

Original language | English |
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Pages (from-to) | 385-395 |

Number of pages | 11 |

Journal | Applied Mathematics and Computation |

Volume | 354 |

DOIs | |

Publication status | Published - 1 Aug 2019 |

## Keywords

- Cubic graph
- Total dominating set
- Total forcing set

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics