Graphs which their certain polynomials have few distinct roots- a survey
  Let G = (V;E) be a simple graph. We consider domination polynomial, matching polynomial and edge cover polynomial of G. Graphs which their polynomials have few roots can give sometimes a very surprising information about the structure of the graph. In this paper we study graphs which their domination polynomial, independence polynomial and edge cover polynomial have few roots. 
Saeid Alikhani
math.CO