## Abstract

A perfect Italian dominating function on a graph G is a function f:V(G)→{0,1,2} satisfying the condition that for every vertex u with f(u)=0, the total weight of f assigned to the neighbors of u is exactly two. The weight of a perfect Italian dominating function is the sum of the weights of the vertices. The perfect Italian domination number of G, denoted γ _{I} ^{p} (G), is the minimum weight of a perfect Italian dominating function of G. We show that if G is a tree on n≥3 vertices, then γ _{I} ^{p} (G)≤[Formula presented]n, and for each positive integer n≡0(mod5) there exists a tree of order n for which equality holds in the bound.

Original language | English |
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Pages (from-to) | 164-177 |

Number of pages | 14 |

Journal | Discrete Applied Mathematics |

Volume | 260 |

DOIs | |

Publication status | Published - 15 May 2019 |

## Keywords

- Italian domination
- Roman domination
- Roman {2}-domination

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics