4 problems

Unique minimal subgraph conjecture. If $G\in\Lambda_n$ and $G$ is not the disconnected union of two graphs in $\Lambda_n$, then there exists a unique graph $G'\in\lambda_n$ such th…

Unicyclic-components conjecture. If $G\in\lambda_n$, then $G$ has unicyclic components.

Non-isomorphic subgraph conjecture. If $G_1\not\cong G_2$ and $G_1,G_2\in\Lambda_n$, then $G$ has a sequence that diverges by order.

Divergence characterization conjecture. The graph $G$ has a sequence that diverges by order if and only if there exists a $k$ such that $HL^k(G)$ has a connected subgraph $G'$ wher…