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.
Sabidussi,On a class of fixed-point-free graphs, Proceedings of the American Mathematical Society9(5), 800 (1958)
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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.