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Asymptotic incidence energy of lattices

Author

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  • Liu, Jia-Bao
  • Pan, Xiang-Feng

Abstract

The energy of a graph G arising in chemical physics, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G. As an analogue to E(G), the incidence energy IE(G), defined as the sum of the singular values of the incidence matrix of G, is a much studied quantity with well known applications in chemical physics. In this paper, based on the results by Yan and Zhang (2009), we propose the incidence energy per vertex problem for lattice systems, and present the closed-form formulae expressing the incidence energy of the hexagonal lattice, triangular lattice, and 33.42 lattice, respectively. Moreover, we show that the incidence energy per vertex of lattices is independent of the toroidal, cylindrical, and free boundary conditions. In particular, the explicit asymptotic values of the incidence energy in these lattices are obtained by utilizing the applications of analysis approach with the help of calculational software.

Suggested Citation

  • Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "Asymptotic incidence energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 193-202.
    • Handle: RePEc:eee:phsmap:v:422:y:2015:i:c:p:193-202
    DOI: 10.1016/j.physa.2014.12.006
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    References listed on IDEAS

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    1. Yan, Weigen & Zhang, Zuhe, 2009. "Asymptotic energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1463-1471.
    2. Liu, Xiaoyun & Yan, Weigen, 2013. "The triangular kagomé lattices revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5615-5621.
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    Citations

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    Cited by:

    1. Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
    2. Song, Jingjing & Wallin, Fredrik & Li, Hailong, 2017. "District heating cost fluctuation caused by price model shift," Applied Energy, Elsevier, vol. 194(C), pages 715-724.
    3. Leurent, Martin & Jasserand, Frédéric & Locatelli, Giorgio & Palm, Jenny & Rämä, Miika & Trianni, Andrea, 2017. "Driving forces and obstacles to nuclear cogeneration in Europe: Lessons learnt from Finland," Energy Policy, Elsevier, vol. 107(C), pages 138-150.
    4. Webber, Phil & Gouldson, Andy & Kerr, Niall, 2015. "The impacts of household retrofit and domestic energy efficiency schemes: A large scale, ex post evaluation," Energy Policy, Elsevier, vol. 84(C), pages 35-43.
    5. Jia-Bao Liu & Mobeen Munir & Amina Yousaf & Asim Naseem & Khudaija Ayub, 2019. "Distance and Adjacency Energies of Multi-Level Wheel Networks," Mathematics, MDPI, vol. 7(1), pages 1-9, January.
    6. Liu, Jia-Bao & Pan, Xiang-Feng, 2016. "Minimizing Kirchhoff index among graphs with a given vertex bipartiteness," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 84-88.
    7. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "A unified approach to the asymptotic topological indices of various lattices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 62-73.
    8. Shin, Kong Joo & Managi, Shunsuke, 2017. "Liberalization of a retail electricity market: Consumer satisfaction and household switching behavior in Japan," Energy Policy, Elsevier, vol. 110(C), pages 675-685.

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