Perfect Roman domination in trees
Document Type
Article
Publication Date
2-19-2018
Abstract
A perfect Roman dominating function on a graph G is a function f:V(G)→{0,1,2} satisfying the condition that every vertex u with f(u)=0 is adjacent to exactly one vertex v for which f(v)=2. The weight of a perfect Roman dominating function f is the sum of the weights of the vertices. The perfect Roman domination number of G, denoted γRp(G), is the minimum weight of a perfect Roman dominating function in G. We show that if G is a tree on n≥3 vertices, then γRp(G)≤[Formula presented]n, and we characterize the trees achieving equality in this bound.
Publication Title
Discrete Applied Mathematics
Volume
236
First Page
235
Last Page
245
Digital Object Identifier (DOI)
10.1016/j.dam.2017.10.027
ISSN
0166218X
Citation Information
Henning, Klostermeyer, W. F., & MacGillivray, G. (2018). Perfect Roman domination in trees. Discrete Applied Mathematics, 236, 235–245. https://doi.org/10.1016/j.dam.2017.10.027