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The magnetic discrete Laplacian inferred from the Gauß–Bonnet operator and application

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Abstract

We consider the notion of \(\chi\)-completeness of a locally finite graph and we extend this notion to the weighted magnetic graph. Moreover, we establish a link between the magnetic adjacency matrix on line graph and the magnetic discrete Laplacian on 1-forms.

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Acknowledgements

The authors thank Sylvain Golénia and Mahmoud Ahmadi for their useful remarks and comments on the text. We wish to express our indebtedness to the referees for their suggestions that have improved significantly the final presentation of this article.

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Authors and Affiliations

  1. Faculty of Sciences of Gafsa, University of Gafsa, 2112, Zarroug, Tunisia

    Nassim Athmouni & Hatem Baloudi

  2. Faculty of Sciences of Sfax, University of Sfax, 3000, Sfax, Tunisia

    Mondher Damak & Marwa Ennaceur

Authors
  1. Nassim Athmouni
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  2. Hatem Baloudi
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  3. Mondher Damak
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  4. Marwa Ennaceur
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Correspondence to Hatem Baloudi.

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Communicated by Marcel de Jeu.

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Athmouni, N., Baloudi, H., Damak, M. et al. The magnetic discrete Laplacian inferred from the Gauß–Bonnet operator and application. Ann. Funct. Anal. 12, 33 (2021). https://doi.org/10.1007/s43034-021-00119-8

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  • DOI: https://doi.org/10.1007/s43034-021-00119-8

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