Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality of Graph Invariants   We study a new set of duality relations between weighted, combinatoric
invariants of a graph $G$. The dualities arise from a non-linear transform
$\mathfrak{B}$, acting on the weight function $p$. We define $\mathfrak{B}$ on
a space of real-valued functions $\mathcal{O}$ and investigate its properties.
We show that three invariants (weighted independence number, weighted
Lov\'{a}sz number, and weighted fractional packing number) are fixed points of
$\mathfrak{B}^{2}$, but the weighted Shannon capacity is not. We interpret
these invariants in the study of quantum non-locality.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph