On the {2}-domination number of rooted product graphs
Abstract
Let G be a nontrivial graph with vertex set V (G). A function f : V (G) → {0, 1, 2} is called a {2}-dominating function on G if ∑u∈NG[v] f(u) ≥ 2 for every v ∈ V (G), where NG[v] represents the closed neighborhood of vertex v ∈ V (G). The {2}-domination number of G is the minimum weight ω(f) = ∑u∈V (G) f(u) among all {2}-dominating functions f on G. In this paper, we obtain a closed formula for the {2}-domination number of rooted product graphs. In particular, we show that in this product graph, this parameter can attain only six possible values, which depend on some domination parameters of the graphs involved in the product. We also characterize the rooted product graphs that satisfy each of these six expressions.
Fields of Study & Subjects
Advanced Graph Theory Research
Graph Labeling and Dimension Problems
Interconnection Networks and Systems
Publication details
- Journal / source
- Quaestiones Mathematicae
- Publisher
- National Inquiry Services Center (NISC)
- Volume
- 49
- Issue
- 5
- Pages
- 671–691
- Publication date
- 30 January 2026
- Language
- EN