Efficient open domination in graph products
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2014-03-01Source
Discrete Mathematics and Theoretical Computer Science - 2014, Vol.16 n.1 pp. 105–120.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 $K_2$. A connection with total domination number is also established
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