Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of k-dominating independent sets   We study the existence and the number of $k$-dominating independent sets in
certain graph families. While the case $k=1$ namely the case of maximal
independent sets - which is originated from Erd\H{o}s and Moser - is widely
investigated, much less is known in general. In this paper we settle the
question for trees and prove that the maximum number of $k$-dominating
independent sets in $n$-vertex graphs is between $c_k\cdot\sqrt[2k]{2}^n$ and
$c_k'\cdot\sqrt[k+1]{2}^n$ if $k\geq 2$, moreover the maximum number of
$2$-dominating independent sets in $n$-vertex graphs is between $c\cdot 1.22^n$
and $c'\cdot1.246^n$. Graph constructions containing a large number of
$k$-dominating independent sets are coming from product graphs, complete
bipartite graphs and with finite geometries. The product graph construction is
associated with the number of certain MDS codes.

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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: q-fin