20.500.12556/RUL-168895 On cubic rainbow domination regular graphs A d-regular graph X is called d-rainbow domination regular or d-RDR, if its d-rainbow domination number γ$_{rd}$(X) attains the lower bound n/2 for d-regular graphs, where n is the number of vertices. In the paper, two combinatorial constructions to construct new d-RDR graphs from existing ones are described and two general criteria for a vertex-transitive d-regular graph to be d-RDR are proven. A list of vertex-transitive 3-RDR graphs of small orders is produced and their partial classification into families of generalized Petersen graphs, honeycomb-toroidal graphs and a specific family of Cayley graphs is given by investigating the girth and local cycle structure of these graphs. rainbow domination regular graphs generalized Petersen graphs honeycomb toroidal graphs cubic vertex-transitive graphs dominacija rednih grafov posplošeni Petersenovi grafi toroidni grafi medenih satov true false true Angleški jezik Slovenski jezik Članek v reviji 2025-05-06 10:54:57 2025-05-06 10:54:58 2025-05-07 11:34:54 0000-00-00 00:00:00 2025 0 0 Str. 26-38 Vol. 373 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 1872-6771 10.1016/j.dam.2025.04.046 234771971 RAZ_Kuzman_Bostjan_2025.pdf RAZ_Kuzman_Bostjan_2025.pdf 1 2B469FDA35C4374B53E9FE5FF72647C5 b0350ccf0bf97b6ddaa5a71c3fb9dd10158302dd433405cedac490d9c1b3bd25 1675f6fe-2a57-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=209978 https://www.sciencedirect.com/science/article/pii/S0166218X25002276 1 9a42b23d-2a56-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=209977 Pedagoška fakulteta 0 0 0