Computing the permanental polynomial of the high level fullerene C70 with high precision

The permanental polynomial of IPR fullerene C-70(D-5h) is computed with quadruple precision arithmetic based on sparse graph on PC in acceptable time. The computing adopts 128 bits to store one float and works well for C-70, while the largest fullerene computed before is C-60, which can be easily obtained now. Some properties of the coefficients and zeroes of the permanental polynomials of IPR fullerenes C-60 and C-70 are also investigated. Computational results show the quadruple precision method can handle permanental polynomial of C-70 and even larger fullerenes, which are of interest in applications.