4 problems

Generalized eigenspace-dimension conjecture. For all positive integers $c,k$, this eigenspace has dimension …

Core conjecture. For any positive integer $k$, the graph $QI(k^2,k)$ is a core.

Maximum-independent-set structure conjecture. For all positive integers $k$, every maximum independent set in $QI(k^2,k)$ is of the form $S_{\{a,b\}}$ for distinct…

Smallest-eigenspace dimension conjecture. For all positive integers $k$, the eigenspace corresponding to this smallest eigenvalue has dimension …