Chen–Zhang's signless Laplacian extremal conjecture for $K_{s,t}$-minor-free graphs

Let $2\leq s\leq t$ and let $G$ be a $K_{s,t}$-minor-free graph of sufficiently large order $n$. Write $q(G)$ for the signless Laplacian spectral radius of $G$, and let $F_{s,t}(n)$ denote the extremal graph defined in the cited source.

Chen–Zhang's conjecture.

$$q(G)\leq q(F_{s,t}(n)),$$

with equality if and only if $G\cong F_{s,t}(n)$.

This conjecture asks for the unique signless Laplacian extremal graph among sufficiently large $K_{s,t}$-minor-free graphs, extending known adjacency-spectral extremal results for this class. The supplied text gives no resolution, so its status remains open.