  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.
