The secure domination number of Cartesian products of small graphs with paths and cycles

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Abstract

The secure domination numbers of the Cartesian products of two small graphs with paths or cycles is determined, as well as for Möbius ladder graphs. Prior to this work, in all cases where the secure domination number has been determined, the proof has either been trivial, or has been derived from lower bounds established by considering different forms of domination. However, the latter mode of proof is not applicable for most graphs, including those considered here. Hence, this work represents the first attempt to determine secure domination numbers via the properties of secure domination itself, and it is expected that these methods may be used to determine further results in the future.

Original languageEnglish
Pages (from-to)32-45
Number of pages14
JournalDiscrete Applied Mathematics
Volume309
DOIs
Publication statusPublished - 15 Mar 2022

Keywords

  • Graph
  • Cycles
  • Paths
  • Cartesian product
  • Secure domination

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