Uniqueness conjecture for general Markov numbers

Let $a$ and $b$ be positive integers with $a<b$. The graph of general Markov numbers is the graph $\mathcal{T}\big((a,a),(b,b)\big)$, whose vertices are triples of integers constructed from the corresponding triple graph. Uniqueness conjecture for general Markov numbers. Each triple at a vertex of $\mathcal{T}\big((a,a),(b,b)\big)$ is uniquely determined by its largest element. The conjecture extends Frobenius's uniqueness conjecture from regular Markov numbers to these general Markov-number graphs. The paper explicitly states that the conjecture is false by defining graphs of general Markov numbers that provide counterexamples.