The permanental polynomials of graphs and matrices

Wei Li
Northwestern Polytechnical University

Heping Zhang
Lanzhou University



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.

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