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On Laplacian Spectrum of Desargues and Pappus Configurations

Year 2023, Issue: 52, 289 - 293, 15.12.2023

Abstract

In this paper, we study Laplacian spectrum of Desargues and Pappus configurations and present some basic spectral properties of these hypergraphs.

References

  • Akça, Z., Günaltılı, I. & Özgür G. (2006 ). On the Fano subplanes of the left semifield plane of order 9. Hacettepe Journal of Mathematics and Statistics, 35(1), 55–61.
  • Ballico, E., Favacchio, G., Guardo, E. & Milazzo, L.(2020). Steiner systems and configurations of points. Designs, Codes and Cryptography, 89, 199–219.
  • Berge, C. (1970). Graphes et hypergraphes. Dunod, Paris.
  • Berge, C. (1973). Graphs and hypergraphs. North-Holland publishing company Amsterdam, 7.
  • Braun, M., Etzion, T., Ostergard,.P., Vardy, A. & Wassermann, A. (2016). Existence of q – analogs of Steiner system. Forum of Mathematics, Pi, 4. doi:10.1017/fmp.2016.5
  • Bretto, A. (2013). Hypergraph theory: An introduction. Mathematical Engineering, Springer.
  • Fallat, S.M., Kirkland, S.J., Molitierno, J.J. & Neumann, M. (2005). On graphs whose Laplacian matrices have distinct integer eigenvalues. Journal of Graph Theory, 50(2), 162–174.
  • Grünbaum, B. (2009). Configurations of the Points and Lines, Graduate Studies in Mathematics, American Mathematical Soc., 103.
  • Molitierno, J.J., Fallat, M.S., Kirkland, S. & Neumann, M. (2005). On graphs whose Laplacian matrices have distinct integer eigenvalues. Journal of Graph Theory, 50(2), 162-174.
  • Naik, N.R., Rao, S.B., Shrikhande S.S. & Singhi N.M. (1982). Intersection graphs of k-uniform linear hypergraphs. European Journal of Combinatorics, (3), 159–172.
  • Ouvrard, X. (2020). Hypergraphs: an introduction and review. (arXiv:2002.05014). arXiv. https://doi.org/10.48550/arXiv.2002.05014
  • Paige, L. & Wexler, C. (1953). A canonical form for incidence matrices of finite projective planes and their associated latin squares. Portugaliae Mathematica, 12(3), 105–112.
  • Zakiyyah, A.Y. (2021). Laplacian integral of particular Steiner system. Engineering, Mathematics and Computer Science Journal, 3(1), 31–32.

Desargues ve Pappus Konfigürasyonlarının Laplasyan Spektrumu Üzerine

Year 2023, Issue: 52, 289 - 293, 15.12.2023

Abstract

Bu makalede, Desargues ve Pappus konfigurasyonlarının Laplasyan spektrumlarını inceliyor ve bu hipergrafların bazı temel spektrum özelliklerini sunuyoruz.

References

  • Akça, Z., Günaltılı, I. & Özgür G. (2006 ). On the Fano subplanes of the left semifield plane of order 9. Hacettepe Journal of Mathematics and Statistics, 35(1), 55–61.
  • Ballico, E., Favacchio, G., Guardo, E. & Milazzo, L.(2020). Steiner systems and configurations of points. Designs, Codes and Cryptography, 89, 199–219.
  • Berge, C. (1970). Graphes et hypergraphes. Dunod, Paris.
  • Berge, C. (1973). Graphs and hypergraphs. North-Holland publishing company Amsterdam, 7.
  • Braun, M., Etzion, T., Ostergard,.P., Vardy, A. & Wassermann, A. (2016). Existence of q – analogs of Steiner system. Forum of Mathematics, Pi, 4. doi:10.1017/fmp.2016.5
  • Bretto, A. (2013). Hypergraph theory: An introduction. Mathematical Engineering, Springer.
  • Fallat, S.M., Kirkland, S.J., Molitierno, J.J. & Neumann, M. (2005). On graphs whose Laplacian matrices have distinct integer eigenvalues. Journal of Graph Theory, 50(2), 162–174.
  • Grünbaum, B. (2009). Configurations of the Points and Lines, Graduate Studies in Mathematics, American Mathematical Soc., 103.
  • Molitierno, J.J., Fallat, M.S., Kirkland, S. & Neumann, M. (2005). On graphs whose Laplacian matrices have distinct integer eigenvalues. Journal of Graph Theory, 50(2), 162-174.
  • Naik, N.R., Rao, S.B., Shrikhande S.S. & Singhi N.M. (1982). Intersection graphs of k-uniform linear hypergraphs. European Journal of Combinatorics, (3), 159–172.
  • Ouvrard, X. (2020). Hypergraphs: an introduction and review. (arXiv:2002.05014). arXiv. https://doi.org/10.48550/arXiv.2002.05014
  • Paige, L. & Wexler, C. (1953). A canonical form for incidence matrices of finite projective planes and their associated latin squares. Portugaliae Mathematica, 12(3), 105–112.
  • Zakiyyah, A.Y. (2021). Laplacian integral of particular Steiner system. Engineering, Mathematics and Computer Science Journal, 3(1), 31–32.
There are 13 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Articles
Authors

Burçin Usta 0000-0002-3183-0619

Ayşe Bayar 0000-0002-2210-5423

Early Pub Date December 29, 2023
Publication Date December 15, 2023
Submission Date October 13, 2023
Acceptance Date December 14, 2023
Published in Issue Year 2023 Issue: 52

Cite

APA Usta, B., & Bayar, A. (2023). On Laplacian Spectrum of Desargues and Pappus Configurations. Avrupa Bilim Ve Teknoloji Dergisi(52), 289-293.