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Efficient Open Domination in Digraph Products

by Dragana Božović 1,2 and Iztok Peterin 1,2,*
Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, 2000 Maribor, Slovenia
Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 496;
Received: 6 February 2020 / Revised: 25 March 2020 / Accepted: 27 March 2020 / Published: 2 April 2020
(This article belongs to the Special Issue Distances and Domination in Graphs)
A digraph D is an efficient open domination digraph if there exists a subset S of V ( D ) for which the open out-neighborhoods centered in the vertices of S form a partition of V ( D ) . In this work we deal with the efficient open domination digraphs among four standard products of digraphs. We present a method for constructing the efficient open domination Cartesian product of digraphs with one fixed factor. In particular, we characterize those for which the first factor has an underlying graph that is a path, a cycle or a star. We also characterize the efficient open domination strong product of digraphs that have factors whose underlying graphs are uni-cyclic graphs. The full characterizations of the efficient open domination direct and lexicographic product of digraphs are also given. View Full-Text
Keywords: efficient open domination; digraphs; products of digraphs efficient open domination; digraphs; products of digraphs
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Božović, D.; Peterin, I. Efficient Open Domination in Digraph Products. Mathematics 2020, 8, 496.

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