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arXiv · 1810.08633

Duality of Graph Invariants

Kaifeng Bu·Weichen Gu·Arthur Jaffe
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Abstract

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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BibTeXRIS

Kaifeng Bu, Weichen Gu, Arthur Jaffe. 2018-10-19. Duality of Graph Invariants. https://arxiv.org/abs/1810.08633

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