Levit–Mandrescu Unimodality Conjecture

The models produced an explicit counterexample: the whiskering of $E_{588} \vee (39K_{11} \sqcup 85K_{12})$, a very well-covered graph on 4,074 vertices, whose independence polynomial $(1+x)^{1449}(1+2x)^{588} + (1+x)^{1913}(1+12x)^{39}(1+13x)^{85} - (1+x)^{2037}$ has a strict local valley at $a_{1095}$. Per the announcement, the search took a few hours once the question was posed.