## Abstract

A double Roman dominating function on a graph G is a function f:V(G)→{0,1,2,3} having the property that every vertex of weight 0 under f has at least one neighbor of weight 3 under f or at least two neighbors of weight 2 under f and every vertex of weight 1 under f has at least one neighbor of weight at least 2 under f. The weight of a double Roman dominating function f is the sum of the weights of the vertices. The double Roman domination number of G, denoted γ _{dR} (G), is the minimum weight of a double Roman dominating function in G. For every graph G, γ _{dR} (G)≤3γ(G), where γ(G) denotes the domination number of G. A graph G satisfying γ _{dR} (G)=3γ(G) is a double Roman graph. In this paper, we characterize the double Roman trees, which answers a problem posed by Beeler et al. (2016).

Original language | English |
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Pages (from-to) | 100-111 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 259 |

DOIs | |

Publication status | Published - 30 Apr 2019 |

## Keywords

- Domination
- Double Roman domination
- Roman domination

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics