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Efficient open domination in graph products

Abstract : A graph G is an efficient open domination graph if there exists a subset D of V(G) for which the open neighborhoods centered in vertices of D form a partition of V(G). We completely describe efficient open domination graphs among lexicographic, strong, and disjunctive products of graphs. For the Cartesian product we give a characterization when one factor is K2.
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Dorota Kuziak, Iztok Peterin, Ismael Gonzalez Yero. Efficient open domination in graph products. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 1 (1), pp.105--120. ⟨10.46298/dmtcs.1267⟩. ⟨hal-01179224⟩

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