Derivatives and real roots of graph polynomials

Abstract: Graph polynomials are polynomials assigned to graphs. Interestingly, they also arise in many areas outside graph theory as well. Many properties of graph polynomials have been widely studied. In this paper, we survey some results on the derivative and real roots of graph polynomials, which have applications in chemistry, control theory and computer science. Related to the derivatives of graph polynomials, polynomial reconstruction of the matching polynomial is also introduced.