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Spectra of generalized windmill networks: Analytical solutions and applications

Author

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  • Yunhua Liao

    (Department of Mathematics, Hunan University of Technology and Business, Changsha 410205, P. R. China†Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Le Havre 76600, France‡Key Laboratory of Hunan Province for Statistical Learning and Intelligent Computation, Changsha 410205, P. R. China)

  • M. A. Aziz-Alaoui

    (#x2020;Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Le Havre 76600, France)

  • Yu Chen

    (#xA7;Department of Mathematics, Hunan Normal University, Changsha 410081, P. R. China)

Abstract

The generalized windmill graphs are good models for many real-world networks. In this paper, we obtain analytic expressions for the eigenvalues of the adjacency matrices and of the Laplacian matrices of the generalized windmill graphs. Using this information, we study some structural and dynamical properties of these graphs. To the end, we investigate the metro networks of four France cities and propose our suggestions for the planning of public transport networks.

Suggested Citation

  • Yunhua Liao & M. A. Aziz-Alaoui & Yu Chen, 2020. "Spectra of generalized windmill networks: Analytical solutions and applications," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(11), pages 1-14, November.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:11:n:s0129183120501594
    DOI: 10.1142/S0129183120501594
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