The normalized Laplacian spectrum of pentagonal graphs and its applications
Received:July 02, 2018  Revised:September 13, 2018
Key Word: Normalized Laplacian spectrum   Multiplicative degree-Kirchhoff index   Kemeny’s constant   The number of spanning trees.  
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Author NameAffiliationE-mail
xu xiaojing Dalian matritime university 18098862621@163.com 
Wang Zhiping Dalian matritime university  
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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.
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