APPLICATIONS OF LAPLACIAN SPECTRA ON A 3-PRISM GRAPH
APPLICATIONS OF LAPLACIAN SPECTRA ON A 3-PRISM GRAPH
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DOI：
10.1142/s0217984914500092
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发表时间：
2014-01
影响因子：
1.9
通讯作者：
Qingyan Ding;Wei-gang Sun;F. Chen
中科院分区：
文献类型：
--
作者：
Qingyan Ding;Wei-gang Sun;F. Chen
本文计算了三棱柱图的Laplacian谱并加以应用。该图既是平面图又是多面体图，属于广义Petersen图。利用该图的正则结构，得到了该图与其初始状态三角形之间的Laplacian矩阵的递归关系，并进一步得到了它们之间的Laplacian特征值的对应关系.利用这些关系，我们得到了所有非零Laplacian特征值的倒数之和与乘积的解析表达式。最后，我们应用这些表达式来计算生成树的数量和平均首次通过时间（MFPT），并看到MFPT与网络大小N的缩放是N2，这是大于一些一致递归树上进行。
In this paper, we calculate the Laplacian spectra of a 3-prism graph and apply them. This graph is both planar and polyhedral, and belongs to the generalized Petersen graph. Using the regular structures of this graph, we obtain the recurrent relationships for Laplacian matrix between this graph and its initial state — a triangle — and further derive the corresponding relationships for Laplacian eigenvalues between them. By these relationships, we obtain the analytical expressions for the product and the sum of the reciprocals of all nonzero Laplacian eigenvalues. Finally we apply these expressions to calculate the number of spanning trees and mean first-passage time (MFPT) and see that the scaling of MFPT with the network size N is N2, which is larger than those performed on some uniformly recursive trees.