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On Idomatic Partitions of Direct Products of Complete Graphs

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Abstract

Independent dominating sets in the direct product of four complete graphs are considered. Possible types of such sets are classified. The sets in which every pair of vertices agree in exactly one coordinate, called T 1-sets, are explicitly described. It is proved that the direct product of four complete graphs admits an idomatic partition into T 1-sets if and only if each factor has at least three vertices and the orders of at least two factors are divisible by 3.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Sandi Klavžar

  2. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000, Maribor, Slovenia

    Sandi Klavžar

  3. Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000, Ljubljana, Slovenia

    Sandi Klavžar & Gašper Mekiš

Authors
  1. Sandi Klavžar
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  2. Gašper Mekiš
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Correspondence to Sandi Klavžar.

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Klavžar, S., Mekiš, G. On Idomatic Partitions of Direct Products of Complete Graphs. Graphs and Combinatorics 27, 713–726 (2011). https://doi.org/10.1007/s00373-010-0997-7

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  • DOI: https://doi.org/10.1007/s00373-010-0997-7

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