Duality of Graph Invariants

@inproceedings{Bu2018DualityOG,
  title={Duality of Graph Invariants},
  author={Kaifeng Bu and Weichen Gu and Arthur Jaffe},
  year={2018}
}
We investigate a non-linear transformation $\mathfrak{B}$ on a function space $\mathcal{O}$ and find necessary and sufficient conditions for it to square to the identity. We use this transform to exhibit dualities between graph invariants: weighted independence numbers, weighted Lov\'{a}sz numbers, and weighted fractional packing numbers. These three invariants are invariant under $\mathfrak{B}^{2}$, but the weighted Shannon capacity is not. Finally, we interpret these invariants in the study… CONTINUE READING

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