Zhang et al.'s unimodality conjecture for cube polynomials of median graphs

Let $G$ be a median graph, and let $C(G,x)$ denote its cube polynomial.

Zhang et al.'s conjecture. The cube polynomial $C(G,x)$ is unimodal.

This conjecture is false: median graphs with non-unimodal cube polynomials are obtained, for example, from an $n$-cube with sufficiently many pendant vertices when $n\geqslant 9$.