# The permanental polynomials of graphs and matrices

**Minisymposium:**
CHEMICAL GRAPH THEORY

**Content:**
P\'{o}lya's problem concerns the conversion of the permanent and
determinant of a matrix. As a generalization of this problem, this
topic focus on the conversion of the permanental polynomial and the
characteristic polynomial. Firstly, we provide a sufficient and
necessary condition for converting the computation of the permanental polynomial of a graph into the computation of the characteristic polynomial of an orientation graph. Then we characterize those matrices whose permanental polynomials can computed by the characteristic polynomials of some matrices.