Unimodality of Domination Polynomial-A Survey

Let g be a graph of order n. a subset s of v (g) is a dominating set of g if every vertex inv (g)ns is adjacent to at least one vertex of s. the domination polynomial of g is the polynomiald(g; x) = pn i=γ(g) d(g; i)xi, where d(g; i) is the number of dominating sets of g of size i, and γ(g) isthe size of a smallest dominating set of g, called the domination number of g. there is a conjecture in[introduction to domination polynomial of a graph, ars combin., 114 (2014) 257-266] which states thatthe domination polynomial of any graph is unimodal. in this paper, we summarize known results on thissubject.