Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Secure Domination Number of Cartesian Products of Small Graphs with
  Paths and Cycles   The secure domination numbers of the Cartesian products of two small graphs
with paths or cycles is determined, as well as for Mobius 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.

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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat