Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dominating sets and Domination polynomials of Cycles   Let G=(V,E) be a simple graph. A set S\subset V is a dominating set of G, if
every vertex in V\S is adjacent to at least one vertex in S. Let {\mathcal
C}_n^i be the family of dominating sets of a cycle C_n with cardinality i, and
let d(C_n,i) = |{\mathcal C}_n^i. In this paper, we construct {\mathcal C}_n^i,
and obtain a recursive formula for d(C_n, i). Using this recursive formula, we
consider the polynomial D(C_n, x) = \sum_{i=1}^n d(C_n, i)x^i, which we call
domination polynomial of cycles and obtain some properties of this polynomial.

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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin