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The Laplacians, Kirchhoff index and complexity of linear Möbius and cylinder octagonal-quadrilateral networks
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  • Jia-bao Liu,
  • Lu-Lu Fang,
  • Qian Zheng,
  • Xin-Bei Peng
Jia-bao Liu
Anhui Xinhua University
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Lu-Lu Fang
Anhui Jianzhu University
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Qian Zheng
Anhui Jianzhu University
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Xin-Bei Peng
Anhui Jianzhu University
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Abstract

Spectrum graph theory not only facilitate comprehensively reflflect the topological structure and dynamic characteristics of networks, but also offer signifificant and noteworthy applications in theoretical chemistry, network science and other fifields. Let Ln (8, 4) represent a linear octagonal-quadrilateral network, consisting of n eight-member ring and n four-member ring. The M¨obius graph Qn(8, 4) is constructed by reverse identifying the opposite edges, whereas cylinder graph Q’n (8, 4) identififies the opposite edges by order. In this paper, the explicit formulas of Kirchhoffff indices and complexity of Qn(8, 4) and Q‘n (8, 4) are demonstrated by Laplacian characteristic polynomials according to decomposition theorem and Vieta’s theorem. In surprise, the Kirchhoffff index of Qn(8, 4)(Q’n (8, 4)) is approximately one-third half of its Wiener index as n → ∞.
03 May 2022Submitted to International Journal of Quantum Chemistry
05 May 2022Submission Checks Completed
05 May 2022Assigned to Editor
20 Jun 2022Reviewer(s) Assigned
16 Jul 2022Review(s) Completed, Editorial Evaluation Pending
25 Jul 2022Editorial Decision: Revise Major
07 Sep 20221st Revision Received
09 Sep 2022Submission Checks Completed
09 Sep 2022Assigned to Editor
12 Sep 2022Reviewer(s) Assigned