Graphs Whose Certain Polynomials Have Few Distinct Roots

Let be a simple graph. Graph polynomials are a well-developed area useful for analyzing properties of graphs. We consider domination polynomial, matching polynomial, and edge cover polynomial of . Graphs which their polynomials have few roots can sometimes give surprising information about the structure of the graph. This paper is primarily a survey of graphs whose domination polynomial, matching polynomial, and edge cover polynomial have few distinct roots. In addition, some new unpublished results and questions are concluded.