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Arithmetic-geometric matrix of graphs and its applications

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  • Zheng, Ruiling
  • Su, Peifeng
  • Jin, Xian’an

Abstract

The chemical applications of the arithmetic-geometric spectral radius ρag(G) and energy Eag(G) of a graph G are explored in this paper. We firstly investigate and compare the prediction power of arithmetic-geometric spectral radius, arithmetic-geometric energy, spectral radii and energies in some other topological descriptors and some physical properties of octane isomers. It is concluded that the arithmetic-geometric spectral radius is a good indicator in forecasting Acentric Factor, Entropy and two topological descriptors SNar, HNar of octane isomers. Since molecular graphs of octane isomers are trees, we study arithmetic-geometric spectral radius of general trees. We prove that for any tree T of order n≥2, 2cosπn+1<ρag(Pn)≤ρag(T)≤ρag(Sn)=n2, with equality holds if and only if T≅Pn (the path of order n) for the lower bound, and if and only if T≅Sn (the star of order n) for the upper bound.

Suggested Citation

  • Zheng, Ruiling & Su, Peifeng & Jin, Xian’an, 2023. "Arithmetic-geometric matrix of graphs and its applications," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    • Handle: RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322008323
    DOI: 10.1016/j.amc.2022.127764
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    References listed on IDEAS

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    1. Yajing Wang & Yubin Gao, 2020. "Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, July.
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