### Abstract

A Roman dominating function of a graph G is a function fV(G)→0,1,2 such that whenever f(v)=0 there exists a vertex u adjacent to v with f(u)=2. The weight of f is w(f)=∑
_{v∈V(G)}
f(v). The Roman domination number
^{γR}
(G) of G is the minimum weight of a Roman dominating function of G. This paper establishes a sharp upper bound on the Roman domination numbers of graphs with minimum degree at least 3. An upper bound on the Roman domination numbers of connected, big-claw-free and big-net-free graphs is also given.

Original language | English (US) |
---|---|

Pages (from-to) | 1386-1391 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 312 |

Issue number | 7 |

DOIs | |

State | Published - Apr 6 2012 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Liu, C-H., & Chang, G. J. (2012). Upper bounds on Roman domination numbers of graphs.

*Discrete Mathematics*,*312*(7), 1386-1391. https://doi.org/10.1016/j.disc.2011.12.021