Alikhani–Peng conjecture on unimodality of domination polynomials

Let $G$ be any graph, and let $D(G)$ denote its domination polynomial, whose coefficient sequence is the sequence of numbers of dominating sets of each cardinality. Alikhani–Peng conjecture. The domination polynomial of any graph is unimodal. Unimodality would give a uniform description of how the numbers of dominating sets vary with their size; the conjecture is cited in the paper as implying unimodality for all spider graphs, but its resolution is not established in the supplied text.