On the Normalized Laplacian and the Number of Spanning Trees of Linear Heptagonal Networks
School of Mathematical Sciences, Anhui Jianzhu University, Hefei 230601, China
School of Mathematics, Southeast University, Nanjing 210096, China
Department of Mathematics and Statistics, South Central University for Nationalities, Wuhan 430074, China
Author to whom correspondence should be addressed.
Received: 22 February 2019 / Revised: 24 March 2019 / Accepted: 25 March 2019 / Published: 28 March 2019
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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
be the linear heptagonal networks. It is interesting to deduce the degree-Kirchhoff index and the number of spanning trees of
due to its complicated structures. In this article, we aimed to first determine the normalized Laplacian spectrum of
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
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MDPI and ACS Style
Liu, J.-B.; Zhao, J.; Zhu, Z.; Cao, J. On the Normalized Laplacian and the Number of Spanning Trees of Linear Heptagonal Networks. Mathematics 2019, 7, 314.
Liu J-B, Zhao J, Zhu Z, Cao J. On the Normalized Laplacian and the Number of Spanning Trees of Linear Heptagonal Networks. Mathematics. 2019; 7(4):314.
Liu, Jia-Bao; Zhao, Jing; Zhu, Zhongxun; Cao, Jinde. 2019. "On the Normalized Laplacian and the Number of Spanning Trees of Linear Heptagonal Networks." Mathematics 7, no. 4: 314.
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