| The Normalized Laplacian Spectrum of Pentagonal Graphs and Its Applications |
| Received:July 02, 2018 Revised:December 10, 2018 |
| Key Words:
normalized Laplacian spectrum multiplicative degree-Kirchhoff index Kemeny's constant the number of spanning trees
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| Fund Project:Supported by the Dalian Science and Technology Project (Grant No.2015A11GX016). |
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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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