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Asymptotic Laplacian-energy-like invariant of lattices

Author

Listed:
  • Liu, Jia-Bao
  • Pan, Xiang-Feng
  • Hu, Fu-Tao
  • Hu, Feng-Feng

Abstract

Let μ1⩾μ2⩾⋯⩾μn denote the Laplacian eigenvalues of a graph G with n vertices. The Laplacian-energy-like invariant, denoted by LEL(G)=∑i=1n-1μi, is a novel topological index. In this paper, we show that the Laplacian-energy-like per vertex of various lattices is independent of the toroidal, cylindrical, and free boundary conditions. Simultaneously, the explicit asymptotic values of the Laplacian-energy-like in these lattices are obtained. Moreover, our approach implies that in general the Laplacian-energy-like per vertex of other lattices is independent of the boundary conditions.

Suggested Citation

  • Liu, Jia-Bao & Pan, Xiang-Feng & Hu, Fu-Tao & Hu, Feng-Feng, 2015. "Asymptotic Laplacian-energy-like invariant of lattices," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 205-214.
    • Handle: RePEc:eee:apmaco:v:253:y:2015:i:c:p:205-214
    DOI: 10.1016/j.amc.2014.12.035
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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. Praba, B. & Saranya, R., 2020. "Application of the graph cellular automaton in generating languages," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 111-121.
    3. Guillermo De Ita Luna & Pedro Bello López & Raymundo Marcial-Romero, 2024. "Counting Rules for Computing the Number of Independent Sets of a Grid Graph," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    4. 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.
    5. Das, Kinkar Ch. & Mojallal, Seyed Ahmad, 2016. "Extremal Laplacian energy of threshold graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 267-280.
    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. Jia-Bao Liu & S. N. Daoud, 2019. "Number of Spanning Trees in the Sequence of Some Graphs," Complexity, Hindawi, vol. 2019, pages 1-22, March.
    9. Shaohui Wang & Chunxiang Wang & Lin Chen & Jia-Bao Liu & Zehui Shao, 2018. "Maximizing and Minimizing Multiplicative Zagreb Indices of Graphs Subject to Given Number of Cut Edges," Mathematics, MDPI, vol. 6(11), pages 1-10, October.

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