Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the signed domination number of some Cayley graphs   A signed dominating function of graph $\Gamma$ is a function $g :V(\Gamma)
\longrightarrow \{-1,1\}$ such that $\sum_{u \in N[v]}g(u) >0$ for each $v \in
V(\Gamma)$. The signed domination number $\gamma_{_S}(\Gamma)$ is the minimum
weight of a signed dominating function on $\Gamma$. Let $G=\langle S \rangle$
be a finite group such that $e \not\in S=S^{-1}$. In this paper, we obtain the
signed domination number of $Cay(S:G)$ based on cardinality of $S$. Also we
determine the classification of group $G$ by $|S|$ and $\gamma_{_S}(Cay(S:G))$.

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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci