Laplacian Integral of Particular Steiner System


  • Alfi Yusrotis Zakiyyah Bina Nusantara University



graph, hypergraph, Laplacian integral, projective plane.


The notion of a hypergraph is motivated by a graph. In graph, every edge contains of two vertices. However, a hypergraph edges contains more than two vertices. In this article use hyperedge to mention edge of hypergraph. A finite projective plane of order n, denoted by  , is a linear intersecting hypergraph. In this research finite projective plane order  is Laplacian integral.


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Author Biography

Alfi Yusrotis Zakiyyah, Bina Nusantara University

Mathematics Department, School of Computer Science


Bretto, A. (2013). Hypergraph theory: An introduction. Mathematical Engineering. Cham:


Ballico, E., Favacchio, G., Guardo, E., & Milazzo, L. (2020). Steiner systems and

configurations of points. Designs, Codes and Cryptography, 1-21.

Braun, M.,Etzion, T., Ostergard,.P., Vardy, A., and Wassermann,A. (2016). Existence of

q – analogs of Steiner system . Forum of Mathematics , Pi, 4, E7. doi : 10.1017/fmp.2016.5

Chee, Y. M., Colbourn, C. J., Dau, H., Gabrys, R., Ling, A. C., Lusi, D., & Milenkovic, O.

(2020). Access balancing in storage systems by labeling partial Steiner systems. Designs, Codes and Cryptography, 88(11), 2361-2376.

Fallat, S.M., Kirkland, S.J., Molitierno, J.J. and Neumann, M., 2005. On graphs whose

Laplacian matrices have distinct integer eigenvalues. Journal of Graph Theory, 50(2),


Li, S., Kang, L., Shan, E., & Dong, Y. (2018). The finite projective plane and the 5-

Uniform linear intersecting hypergraphs with domination number four. Graphs and

Combinatorics, 34(5), 931-945.

Rodriguez, J. A. (2003). On the Laplacian spectrum and walk-regular hypergraphs. Linear

and Multilinear Algebra, 51(3), 285-297.

Zakiyyah, A.Y., Garminia, H., Salman, A.N.M. On the characterization of Laplacian integral complete tripartite hypergraphs Far East Journal of Mathematical Sciences

(9), 2133-2142 | vol: | issue : | 2017






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