Partitioning the vertex set of ▫$G$▫ to make ▫$G \Box H$▫ an efficient open domination graphKraner Šumenjak, Tadeja (Avtor) Peterin, Iztok (Avtor) Rall, Douglas F. (Avtor) Tepeh, Aleksandra (Avtor) efficient open dominationCartesian productvertex labelingtotal dominationA graph is an efficient open domination graph if there exists a subset of vertices whose open neighborhoods partition its vertex set. We characterize those graphs ▫$G$▫ for which the Cartesian product ▫$G \Box H$▫ is an efficient open domination graph when ▫$H$▫ is a complete graph of order at least 3 or a complete bipartite graph. The characterization is based on the existence of a certain type of weak partition of ▫$V(G)$▫. For the class of trees when ▫$H$▫ is complete of order at least 3, the characterization is constructive. In addition, a special type of efficient open domination graph is characterized among Cartesian products ▫$G \Box H$▫ when ▫$H$▫ is a 5-cycle or a 4-cycle.20162017-07-10 12:00:15Znanstveno delo66784sl