25. 用红白蓝三色对一个正五边形的顶点进行着色, 求使得两顶点为红色, 两顶点为白色,一顶点为蓝色的不等价的着色数.
$$
\begin{array}{l}
\text { 25. } D=\{1,2,3,4,5\}, R=\{r, w, b\} \text {. } \\
G=\left\{e, \rho_{5}, \rho_{5}^{2}, \rho_{5}^{3}, \rho_{5}^{4}, \tau_{1}, \tau_{2}, \tau_{3}, \tau_{4}, \tau_{5}\right\}, \\
P_{G}\left(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\right)=\frac{1}{10}\left(x_{1}^{5}+4 x_{5}+5 x_{1} x_{2}^{2}\right) \text {, } \\
P_{G}\left((r+w+b),\left(r^{2}+w^{2}+b^{2}\right), \cdots,\left(r^{5}+w^{5}+b^{5}\right)\right) \\
=\frac{1}{10}\left[(r+w+b)^{5}+4\left(r^{5}+w^{5}+b^{5}\right)\right. \\
\left.+5(r+w+b)\left(r^{2}+w^{2}+b^{2}\right)^{2}\right], \\
\end{array}
$$

其中 $r^{2} w^{2} b$ 的系数为 $\frac{1}{10}\left(\frac{5!}{2!\times 2!\times 1!}+5 \times 2\right)=4$.