Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetric inequalities for eigenvalues of the Laplacian on cycles
  with fixed resistance metric   For cycles with non-negative weights on its edges, we define its global
resistance as the sum of the distances given by the effective resistance metric
between adjacent vertices. We prove the following result: for the Laplace
operator on the 3-cycle with global resistance equal to a given constant, the
maximal value of the smallest positive eigenvalue and the minimal value of the
largest eigenvalue, are both attained if and only if all the weights are equal
to each other.

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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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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: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th