Discrete Mathematics & Theoretical Computer Science, Vol 16, No 1 (2014)

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Efficient open domination in graph products

Dorota Kuziak, Iztok Peterin, Ismael Gonzalez Yero


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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