## Abstract

Given a graph G and a set S⊆ V(G) a vertex v is said to be _{3} -dominated by a vertex w in S if either v=w, or v∉ S and there exists a vertex u in V(G)-S such that P:wuv is a path in G. A set S⊆ V(G)is an _{3} -dominating set of G if every vertex v is _{3} -dominated by a vertex w in S.The _{3} -domination number of G, denoted by γ F_{3}(G), is the minimum cardinality of an _{3} -dominating set of G. In this paper, we study the _{3} -domination of Cartesian product of graphs, and give formulas to compute the _{3} -domination number of P_{m}×P_{n}and P_{m}× C_{n}for special m,n.

Original language | English |
---|---|

Pages (from-to) | 400-413 |

Number of pages | 14 |

Journal | Journal of Combinatorial Optimization |

Volume | 28 |

Issue number | 2 |

DOIs | |

State | Published - Aug 2014 |

## Keywords

- Cartesian product
- Cycle
- Domination
- Path

## Fingerprint

Dive into the research topics of 'F_{3}-domination problem of graphs'. Together they form a unique fingerprint.