Nonisomorphic trees are not LV-equivalent

A tree is a hypergraph whose hyperedges all have size two, and an LV-system is a Lotka–Volterra system associated with such a hypergraph. Two associated systems are LV-equivalent when they lie in the same equivalence class induced by linear transformations of the associated Lotka–Volterra systems. Tree non-equivalence conjecture. Nonisomorphic trees are not LV-equivalent. The statement has been confirmed for trees of order smaller than nine; its validity for larger orders remains open.