On cubic rainbow domination regular graphsKuzman, Boštjan (Avtor) rainbow domination regular graphsgeneralized Petersen graphshoneycomb toroidal graphscubic vertex-transitive graphsA 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.20252025-05-06 10:54:57Članek v reviji168895sl