The normalized Laplacian spectrum of quadrilateral graphs and its applications
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摘要
The quadrilateral graph Q(G) of G is obtained from G by replacing each edge in G with two parallel paths of lengths 1 and 3. In this paper, we completely describe the normalized Laplacian spectrum on Q(G) for any graph G. As applications, the significant formulae to calculate the multiplicative degree-Kirchhoff index, the Kemeny’s constant and the number of spanning trees of Q(G) and the quadrilateral iterative graph Qr(G) are derived.
论文关键词：Quadrilateral,Normalized Laplacian spectrum,Multiplicative degree-Kirchhoff index,Kemeny’s constant,The number of spanning trees
论文评审过程：Received 18 July 2016, Revised 18 October 2016, Accepted 31 October 2016, Available online 12 November 2016, Version of Record 2 December 2016.
论文官网地址：https://doi.org/10.1016/j.amc.2016.10.041
