## Abstract

In this paper, we study a dynamic coloring of the vertices of a graph G that starts with an initial subset S of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non-colored neighbor to be colored. The initial set S is a zero forcing set of G if, by iteratively5 applying the forcing process, every vertex in G becomes colored. The zero forcing number of G is the minimum cardinality of a zero forcing set of G. In this paper, we prove that if G≠ K_{4} is a connected cubic graph, then the zero forcing number of G is bounded above by twice its domination number, where the domination number of G is the minimum cardinality of a set of vertices of G such that every vertex not in S is adjacent to some vertex in S.

Original language | English |
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Pages (from-to) | 553-577 |

Number of pages | 25 |

Journal | Journal of Combinatorial Optimization |

Volume | 41 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2021 |

## Keywords

- Dominating set
- Domination number
- Zero forcing number
- Zero forcing set

## ASJC Scopus subject areas

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