The odd-graph Thurston–Bennequin symmetry conjecture

Let $O_n$ denote the odd graph with parameter $n\geq 2$. A graph is TB-symmetrical when its total Thurston–Bennequin number admits the symmetry described in the paper. Odd-graph TB-symmetry conjecture. The odd graph $O_n$ is TB-symmetrical for any $n\geq 2$. This conjecture concerns the classification of TB-symmetrical graphs; it is resolved for $n=2,3$, while the general case remains open.