The $D^2_n$ non-TRVG conjecture

Let $D^2_n$ denote the graph in the paper with parameter $a=2$ and $n$ vertices. A non-TRVG is a graph that is not a transparent rectangle visibility graph. The conjecture concerns integers satisfying

$$n\ge 10.$$

The $D^2_n$ non-TRVG conjecture. $D^2_n$ is a non-TRVG when $n\ge10$.

The paper shows that $D^2_n$ is a TRVG for $n\le 8$ and gives a toroidal representation for $D^2_{10}$, while reporting no planar representation; the asserted non-TRVG result for all $n\ge10$ remains open.