LC-orbit minimum-degree conjecture for the interlace polynomial Q

Let $G$ be a graph on $n$ vertices, and let $\delta$ be the minimum vertex degree among all graphs in the LC orbit of $G$. Suppose that there is no graph $G'$ on $n$ vertices with

$$Q(G',4)<Q(G,4).$$

LC-orbit minimum-degree conjecture. Then there is no graph on $n$ vertices whose minimum vertex degree among all graphs in its LC orbit is greater than $\delta$. The statement proposes a relation between minimizing $Q(G,4)$ and maximizing the minimum degree within a local-complementation orbit; the paper presents it as an open conjecture supported by the computational data in its tables.