On the double Roman domination in generalized Petersen graphs P(5k, k)Rupnik Poklukar, Darja (Avtor) Žerovnik, Janez (Avtor) double Roman dominationgeneralized Petersen graphdischarging methodgraph coverdouble Roman graphA 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) = 0 is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and every vertex u with f(u) = 1 is adjacent to at least one vertex assigned 2 or 3. The weight of f equals w(f) = ∑$_{v∈V}$ f(v). The double Roman domination number γ$_{dR}$(G) of a graph G equals the minimum weight of a double Roman dominating function of G. We obtain closed expressions for the double Roman domination number of generalized Petersen graphs P(5k, k). It is proven that γ$_{dR}$(P(5k, k)) = 8k for k ≡ 2, 3 mod 5 and 8k ≤ γ$_{dR}$(P(5k, k)) ≤ 8k + 2 for k ≡ 0, 1, 4 mod 5. We also improve the upper bounds for generalized Petersen graphs P(20k, k).20222022-01-17 11:46:42Članek v reviji134466UDK: 519.17ISSN pri članku: 2227-7390DOI: 10.3390/math10010119COBISS_ID: 93020931sl