2000 character limit reached
Duality of Graph Invariants (1810.08633v2)
Published 19 Oct 2018 in math.FA, math-ph, math.CO, and math.MP
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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.