The authors conjecture that every LOCC-monotone multi-invariant is labeled by a finite Coxeter group and prove this for the A_n, B_n, D_n and I_n families.
Structural characterization of Cayley graphs
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abstract
We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle language, or just the same elementary cycle language. Under the assumption of the axiom of choice, we characterize the Cayley graphs for all group subsets as the deterministic, co-deterministic, vertex-transitive simple graphs.
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Monotones from multi-invariants: a classification
The authors conjecture that every LOCC-monotone multi-invariant is labeled by a finite Coxeter group and prove this for the A_n, B_n, D_n and I_n families.