Dominant-eigenvalue pattern conjecture for generalized Petersen limiting curves

For a family of generalized Petersen graphs $G(nk,k)$, let $Q_c(k)$ be the real crossing value and let $\mu_{k+1,\ell,(\ell),\star}$ denote the indicated dominant eigenvalues. Dominant-eigenvalue pattern conjecture. For $k\geq4$, the dominant eigenvalue on regions intersecting the real $Q$-axis is given by the five-case formula in the source, and consequently $Q=1,3$ and, when $Q_c(k)>5$, $Q=5$ are isolated limiting points, while $Q=2,4,Q_c(k)$ are non-isolated limiting points. The source says the conjecture is also valid for $k=3$ after omitting the empty $\mu_{k+1,3,(3),\star}$ region, and reports validation for the studied cases.