In this paper, the Laplacian matrix of an n-prism network $U_g^n$ and its applications are studied. Firstly, the relation between the Laplacian matrix of $U_g^n$ and that of $U_0^n$ is established. Secondly, the analytical expression for the product of all the nonzero Laplacian eigenvalues of $U_g^n$ is obtained. At the same time, the sum of the reciprocals of all these nonzero Laplacian eigenvalues is deduced. Through these closed analytical results, the expressions for MFPT, the Kirchhoff index and the number of spanning trees of an n-prism network are determined, respectively. Finally, a few numerical examples are given to illustrate the results.

本文研究了n棱镜网络的Laplacian矩阵${ü}_G^{ñ}$及其应用进行了研究。首先，拉普拉斯矩阵之间的关系${ü}_G^{ñ}$ 和 ${ü}_0^{ñ}$成立。其次，所有非零拉普拉斯特征值乘积的解析表达式${ü}_G^{ñ}$获得。同时，推导所有这些非零拉普拉斯特征值的倒数之和。通过这些封闭的分析结果，分别确定了MFPT的表达式，基尔霍夫指数和n棱镜网络的生成树数。最后，给出了一些数值示例来说明结果。