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Efficient Open Domination in Digraph Products

Author

Listed:
  • Dragana Božović

    (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)

  • Iztok Peterin

    (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)

Abstract

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.

Suggested Citation

  • Dragana Božović & Iztok Peterin, 2020. "Efficient Open Domination in Digraph Products," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:496-:d:340423
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    References listed on IDEAS

    as
    1. Iztok Peterin & Ismael G. Yero, 2019. "Efficient closed domination in digraph products," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 130-149, July.
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