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The Laplacians and Normalized Laplacians of the linear chain networks and applications
  • Jia-bao Liu,
  • Kang Wang,
  • Jiao-Jiao Gu
Jia-bao Liu
Anhui Xinhua University

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Kang Wang
Anhui Jianzhu University South Campus
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Jiao-Jiao Gu
Anhui Jianzhu University South Campus
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In recent years, spectrum analysis and computation have developed rapidly in order to explore and characterize the properties of network sciences. Let Ln be obtained from the transformation of the graph L6,4,4 n , which obtained by attaching crossed two four-membered rings to the terminal of crossed phenylenes. Firstly, we study the (nomalized) Laplacian spectrum of Ln based on the decomposition theorem for the corresponding matrices. Secondly, we obtain the closed-term fomulas for the (multiplicative degree) Kirchhoff index and the number of spanning trees from the relationship between roots and coefficients in linear chain networks. Finally, we are surprised to find that the (multiplicative degree) Kirchhoff index of Ln is nearly to one quarter of its (Gutman) Wiener index when n tends to infinity.