20.500.12556/RUL-133672 Independent rainbow domination numbers of generalized Petersen graphs P(n, 2) and P(n, 3) We obtain new results on independent 2- and 3-rainbow domination numbers of generalized Petersen graphs P(n, k) for certain values of n,k ∈ $\mathbb{N}$. By suitably adjusting and applying a well established technique of tropical algebra (path algebra) we obtain exact 2-independent rainbow domination numbers of generalized Petersen graphs P(n, 2) and P(n, 3) thus confirming a conjecture proposed by Shao et al. In addition, we compute exact 3-independent rainbow domination numbers of generalized Petersen graphs P(n, 2). The method used here is developed for rainbow domination and for Petersen graphs. However, with some natural modifications, the method used can be applied to other domination type invariants, and to many other classes of graphs including grids and tori. independent rainbow domination independent rainbow domination number generalized Petersen graphs tropical algebra path algebra neodvisna mavrična dominacija neodvisno mavrično dominacijsko število posplošeni Petersonovi grafi tropska algebra algebra poti true false true Angleški jezik Slovenski jezik Članek v reviji 2021-12-08 10:36:12 2021-12-08 10:36:13 2022-09-13 03:51:58 0000-00-00 00:00:00 2020 0 0 13 str. iss. 6, art. 996 Vol. 8 June 2020 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 2227-7390 10.3390/math8060996 20459011 RAZ_Gabrovsek_Bostjan_2020.pdf RAZ_Gabrovsek_Bostjan_2020.pdf 1 28237783F4AE8978CFCC708881FE08E5 a351329e90dac9db25d75fab7319907e10b3e7f934d91c8ce863ad60186b7989 7cf8307f-580a-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=151930 https://www.mdpi.com/2227-7390/8/6/996 0 4aa49c7e-580a-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=151929 Fakulteta za strojništvo 0 0 0