Study on the normalized Laplacian of a penta-graphene with applications |
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Authors: | Qishun Li Shahid Zaman Wanting Sun Jawad Alam |
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Institution: | 1. School of Electrical Engineering, Beijing Jiaotong University, Beijing, China;2. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, China;3. Department of Mathematics, University of Sialkot, Sialkot, Pakistan |
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Abstract: | Let L n denote a linear pentagonal chain with 2n pentagons. The penta-graphene (penta-C), denoted by R n is the graph obtained from L n by identifying the opposite lateral edges in an ordered way, whereas the pentagonal Möbius ring is the graph obtained from the L n by identifying the opposite lateral edges in a reversed way. In this paper, through the decomposition theorem of the normalized Laplacian characteristic polynomial and the relationship between its roots and the coefficients, an explicit closed-form formula of the multiplicative degree-Kirchhoff index (resp. Kemeny's constant, the number of spanning trees) of R n is obtained. Furthermore, it is interesting to see that the multiplicative degree-Kirchhoff index of R n is approximately of its Gutman index. Based on our obtained results, all the corresponding results are obtained for . |
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Keywords: | multiplicative degree-Kirchhoff index normalized Laplacian penta-graphene spanning tree |
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