Almost unimodal and real-rooted graph polynomials

It is well known that the coefficients of matching polynomial are unimodal. Unimodality (or their absolute values) other graph polynomials has been studied as well. One way to prove unimodality real-rootedness. Recently I. Beaton and J. Brown (2020) proved for almost all graphs domination form a unimodal sequence, C. Barton, D. Pike forest (aka acyclic polynomial) real-rooted iff G forest. Let A be property, let ai(G) number induced subgraphs order i which in A. Inspired by results we prove: Theorem: If complement hereditary then G(n,p) sequence property contains not clique or clique, PA(G;x)=∑iai(G)xi G∈A.