20.500.12556/RUL-134471 Double Roman graphs in P(3k, k) A double Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2, 3} with the properties that if f(u) = 0, then vertex u is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and if f(u) = 1, then vertex u 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 is the minimum weight of a double Roman dominating function of G. A graph is said to be double Roman if γ$_{dR}$(G) = 3γ(G), where γ(G) is the domination number of G. We obtain the sharp lower bound of the double Roman domination number of generalized Petersen graphs P(3k, k), and we construct solutions providing the upper bounds, which gives exact values of the double Roman domination number for all generalized Petersen graphs P(3k, k). This implies that P(3k, k) is a double Roman graph if and only if either k ≡ 0 (mod 3) or k ∈ {1, 4}. double Roman domination generalized Petersen graph double Roman graph dvojna rimska dominacija posplošeni Petersenovi grafi dvojno rimski grafi true false true Angleški jezik Slovenski jezik Članek v reviji 2022-01-17 13:18:51 2022-01-17 13:18:52 2022-09-13 03:55:21 0000-00-00 00:00:00 2021 0 0 18 str. iss. 4, art. 336 Vol. 9 Feb. 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17(045) 2227-7390 10.3390/math9040336 50563587 RAZ_Shao_Zehui_2021.pdf RAZ_Shao_Zehui_2021.pdf 1 3B7665528AF889D7A808C464C554E19A f15cc2281dde0f3435ab01693d3493ae8cb097d9efa17d2488358da45dde652d 783d1d5a-932c-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=153956 https://www.mdpi.com/2227-7390/9/4/336 1 71b18932-778f-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=152948 Fakulteta za strojništvo 0 0 0