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- Title
Double Roman Domination in Generalized Petersen Graphs P (ck , k).
- Authors
Rupnik Poklukar, Darja; Žerovnik, Janez
- Abstract
A double Roman dominating function on a graph G = (V , E) is a function f : V → { 0 , 1 , 2 , 3 } , satisfying the condition that every vertex u for which f (u) = 1 is adjacent to at least one vertex assigned 2 or 3, and every vertex u with f (u) = 0 is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2. The weight of f equals the sum w (f) = ∑ v ∈ V f (v) . The minimum weight of a double Roman dominating function of G is called the double Roman domination number γ d R (G) of a graph G. We obtain tight bounds and in some cases closed expressions for the double Roman domination number of generalized Petersen graphs P (c k , k) . In short, we prove that γ d R (P (c k , k)) = 3 2 c k + ε , where lim c → ∞ , k → ∞ ε c k = 0 .
- Subjects
PETERSEN graphs; DOMINATING set; CHARTS, diagrams, etc.
- Publication
Symmetry (20738994), 2022, Vol 14, Issue 6, pN.PAG
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym14061121