On the Normalized Laplacian and the Number of Spanning Trees of Linear Heptagonal Networks

Jia-Bao Liu, Jing Zhao, Zhongxun Zhu and Jinde Cao
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Jia-Bao Liu: School of Mathematical Sciences, Anhui Jianzhu University, Hefei 230601, China
Jing Zhao: School of Mathematical Sciences, Anhui Jianzhu University, Hefei 230601, China
Zhongxun Zhu: Department of Mathematics and Statistics, South Central University for Nationalities, Wuhan 430074, China
Jinde Cao: School of Mathematics, Southeast University, Nanjing 210096, China

Mathematics, 2019, vol. 7, issue 4, 1-15

Abstract: The normalized Laplacian plays an important role on studying the structure properties of non-regular networks. In fact, it focuses on the interplay between the structure properties and the eigenvalues of networks. Let H n be the linear heptagonal networks. It is interesting to deduce the degree-Kirchhoff index and the number of spanning trees of H n due to its complicated structures. In this article, we aimed to first determine the normalized Laplacian spectrum of H n by decomposition theorem and elementary operations which were not stated in previous results. We then derived the explicit formulas for degree-Kirchhoff index and the number of spanning trees with respect to H n .

Keywords: normalized Laplacian; resistance distance; degree-Kirchhoff index; spanning tree (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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