On Laplacian Spectrum of Desargues and Pappus Configurations

Yıl 2023, Sayı: 52, 289 - 293, 15.12.2023

Burçin Usta , Ayşe Bayar

Öz

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

Anahtar Kelimeler

Hypergraph, Desargues Configuration, Pappus Configuration, Laplacian spectrum .

Desargues ve Pappus Konfigürasyonlarının Laplasyan Spektrumu Üzerine

Öz

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

Anahtar Kelimeler

Hipergraf, Desargue Konfigürasyonu, Pappus Konfigürasyonu, Laplasyan spektrum.

Kaynakça

• 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.