The Normalized Laplacian Spectrum of Pentagonal Graphs and Its Applications  

作　　者：Xiaojing XU Peiwen WANG Zhiping WANG 

机构地区：[1]Faculty of Science , Dalian Maritime University, Liaoning 116026, P. R. China [2]College of Shipping Economics and Management, Dalian Maritime University, Liaoning 116026, P. R. China

出　　处：《Journal of Mathematical Research with Applications》2019年第4期343-352,共10页数学研究及应用（英文版）

基　　金：Supported by the Dalian Science and Technology Project(Grant No.2015A11GX016)

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-Kirchhoffindex, Kemeny’s constant and number of spanning trees.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-Kirchhoffindex, Kemeny’s constant and number of spanning trees.

关 键 词：normalized LAPLACIAN spectrum MULTIPLICATIVE degree-Kirchhoff index Kemeny's CONSTANT the number of SPANNING trees 

分 类 号：O1[理学—数学]