五边形图的标准化的拉普拉斯谱及其应用

The Normalized Laplacian Spectrum of Pentagonal Graphs and Its Applications

中文关键词:  标准化的拉普拉斯谱  倍增度基尔霍夫指数  凯梅尼常数  生成树的个数

英文关键词:normalized Laplacian spectrum  multiplicative degree-Kirchhoff index  Kemeny's constant  the number of spanning trees

中文摘要:

      一个图的标准化的拉普拉斯特征值对图在结构性质和一些相关的动力学方面提供了信息,尤其在相关的随机过程方面. 在这篇文章中,我们给出了由一个简单连通图迭代生成的五边形图的标准化的拉普拉斯谱.在应用方面,我们得到了关于倍增度基尔霍夫指数,凯梅尼常数和生成树的个数的重要公式.

英文摘要:

      The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to random walks. In this paper, we give the spectra of the normalized Laplacian of iterated pentagonal of a simple connected graph. As an application, we also find the significant formulae for their multiplicative degree-Kirchhoff index, Kemeny's constant and number of spanning trees.