Explicit determination of three invariants associated with random walks on n-prism networks

摘要

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.

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