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Efficient closed domination in digraph products

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Abstract

A digraph D is an efficient closed domination digraph if there exists a subset S of V(D) for which the closed out-neighborhoods centered in vertices of S form a partition of V(D). In this work we deal with efficient closed domination digraphs among several product of digraphs. We completely describe the efficient closed domination digraphs among lexicographic and strong products of digraphs. We characterize those direct products of digraphs that are efficient closed domination digraphs, where factors are either two cycles or two paths. Among Cartesian product of digraphs, we describe all such efficient closed domination digraphs such that they are a Cartesian product digraph either with a cycle or with a star.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, 2000, Maribor, Slovenia

    Iztok Peterin

  2. Departamento de Matemáticas, Escuela Politécnica Superior de Algeciras, Universidad de Cádiz, Av. Ramón Puyol s/n, 11202, Algeciras, Spain

    Ismael G. Yero

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  1. Iztok Peterin
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  2. Ismael G. Yero
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Correspondence to Iztok Peterin.

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Iztok Peterin was partially supported by ARRS Slovenia under the Grants P1-0297 and J1-9109.

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Peterin, I., Yero, I.G. Efficient closed domination in digraph products. J Comb Optim 38, 130–149 (2019). https://doi.org/10.1007/s10878-018-0370-y

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