Guiduli–Mohar asymptotic structure conjecture for minimum-degree extremal graphs

Let $G$ be a $\mu$-minimal graph with minimum degree $\delta(G)=d$, where $\mu$ is algebraic connectivity. A graph is path-like when its block-tree is a path.

Guiduli–Mohar conjecture. The graph $G$ is path-like, and, except for some blocks near each end, it has the same structure as Figure Mohar.

This is the general-$n$ structural version of the preceding Guiduli–Mohar conjecture. The source does not report a resolution of the claim; its precise block structure depends on the cited figure.