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The normalized Laplacian spectrum of quadrilateral graphs and its applications

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  • Li, Deqiong
  • Hou, Yaoping

Abstract

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.

Suggested Citation

  • Li, Deqiong & Hou, Yaoping, 2017. "The normalized Laplacian spectrum of quadrilateral graphs and its applications," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 180-188.
    • Handle: RePEc:eee:apmaco:v:297:y:2017:i:c:p:180-188
    DOI: 10.1016/j.amc.2016.10.041
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    References listed on IDEAS

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    1. Xie, Pinchen & Zhang, Zhongzhi & Comellas, Francesc, 2016. "The normalized Laplacian spectrum of subdivisions of a graph," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 250-256.
    2. Xie, Pinchen & Zhang, Zhongzhi & Comellas, Francesc, 2016. "On the spectrum of the normalized Laplacian of iterated triangulations of graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1123-1129.
    3. Huang, Jing & Li, Shuchao & Li, Xuechao, 2016. "The normalized Laplacian, degree-Kirchhoff index and spanning trees of the linear polyomino chains," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 324-334.
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    Cited by:

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    2. Zong, Yue & Dai, Meifeng & Wang, Xiaoqian & He, Jiaojiao & Zou, Jiahui & Su, Weiyi, 2018. "Network coherence and eigentime identity on a family of weighted fractal networks," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 184-194.
    3. Ma, Xiaoling & Bian, Hong, 2019. "The normalized Laplacians, degree-Kirchhoff index and the spanning trees of hexagonal Möbius graphs," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 33-46.
    4. Huang, Jing & Li, Shuchao, 2018. "The normalized Laplacians on both k-triangle graph and k-quadrilateral graph with their applications," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 213-225.
    5. Liao, Yunhua & Aziz-Alaoui, M.A. & Zhao, Junchan & Hou, Yaoping, 2019. "The behavior of Tutte polynomials of graphs under five graph operations and its applications," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.

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