20.500.12556/RUL-134466 On the double Roman domination in generalized Petersen graphs P(5k, k) 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) = 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). double Roman domination generalized Petersen graph discharging method graph cover double Roman graph dvojna rimska dominacija posplošeni Petersonovi grafi pokritja grafov true false true Angleški jezik Slovenski jezik Članek v reviji 2022-01-17 11:46:42 2022-01-17 11:46:43 2022-09-13 03:55:20 0000-00-00 00:00:00 2022 0 0 19 str. iss. 1, art. 119 Vol. 10 Jan. 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 2227-7390 10.3390/math10010119 93020931 RAZ_Rupnik_Poklukar_Darja_2022.pdf RAZ_Rupnik_Poklukar_Darja_2022.pdf 1 BDE2F4119A3A901B0BD32F748BE13B22 12b045b21acd290fb6358a7845d652968b5ffed9c1ed1c1ed0305154b46086d6 32126c6c-7783-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=152939 https://www.mdpi.com/2227-7390/10/1/119 1 92594c7c-7782-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=152938 Fakulteta za strojništvo 0 0 0