The Normalized Laplacian Spectrum of Pentagonal Graphs and Its Applications
Received:July 02, 2018  Revised:December 10, 2018
Key Word: normalized Laplacian spectrum   multiplicative degree-Kirchhoff index   Kemeny's constant   the number of spanning trees  
Fund ProjectL:Supported by the Dalian Science and Technology Project (Grant No.2015A11GX016).
Author NameAffiliation
Xiaojing XU Faculty of Science , Dalian Maritime University, Liaoning 116026, P. R. China 
Peiwen WANG College of Shipping Economics and Management, Dalian Maritime University, Liaoning 116026, P. R. China 
Zhiping WANG Faculty of Science , Dalian Maritime University, Liaoning 116026, P. R. China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:2095-2651.2019.04.002
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