Alikhani–Peng unimodality conjecture for domination sequences

Let $G$ be a finite simple undirected graph with vertex set $V(G)$, let $n=|V(G)|$, and let $d_k(G)$ denote the number of dominating sets of $G$ of size $k$. The polynomial

$$D(G,x)=\sum_{k=0}^{n}d_k(G)x^k$$

records these numbers. Alikhani–Peng unimodality conjecture. For every finite graph $G$, the domination sequence $(d_k(G))_{k=0}^{n}$ is unimodal. This conjecture predicts a strong shape constraint on the coefficients of domination polynomials, complementing known structural results from graph operations and studies of their roots. Its general status is unresolved in the supplied source.