Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: All Terminal Reliability Roots of Smallest Modulus   Given a connected graph $G$ whose vertices are perfectly reliable and whose
edges each fail independently with probability $q\in[0,1],$ the
\textit{(all-terminal) reliability} of $G$ is the probability that the
resulting subgraph of operational edges contains a spanning tree (this
probability is always a polynomial in $q$). The location of the roots of
reliability polynomials has been well studied, with particular interest in
finding those with the largest moduli. In this paper, we will discuss a related
problem -- among all reliability polynomials of graphs on $n$ vertices, which
has a root of smallest modulus? We prove that, provided $n \geq 3$, the roots
of smallest moduli occur precisely for the cycle graph $C_n$, and the root is
unique.

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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: physics