Title
Perfect Italian Domination in Trees
Document Type
Article
Publication Date
5-15-2019
Description
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 Ip (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 Ip (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.
Citation Information
Haynes, Teresa W.; and Henning, Michael A.. 2019. Perfect Italian Domination in Trees. Discrete Applied Mathematics. Vol.260 164-177. https://doi.org/10.1016/j.dam.2019.01.038 ISSN: 0166-218X