Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some new results on domination roots of a graph   Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is
the polynomial $D(G,\lambda)=\sum_{i=0}^{n} d(G,i) \lambda^{i}$, where $d(G,i)$
is the number of dominating sets of $G$ of size $i$. Every root of
$D(G,\lambda)$ is called the domination root of $G$. We present families of
graphs whose their domination polynomial have no nonzero real roots. We observe
that these graphs have complex domination roots with positive real part. Then,
we consider the lexicographic product of two graphs and obtain a formula for
domination polynomial of this product. Using this product, we construct a
family of graphs which their domination roots are dense in all of $\mathbb{C}$.

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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: physics
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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: hep-ex