Integral Hypergraphs Of The Cartesian Product Of Fano Plane And Latin Squares Of Order 3
DOI:
https://doi.org/10.25077/jmua.14.4.333-340.2025Keywords:
Cartesian Product, Fano Plane, and Latin SquaresAbstract
Operasi pada hipergraf adalah suatu cara untuk mengkonstruksi suatu hipergraf dengan struktur yang lebih besar. Salah satu operasi pada hipergraf yang biasa dipelajari adalah operasi kali Kartesius. Suatu hipergraf dikatakan integral jika semua nilai karakteristik dari matriks ketetanggaannya adalah bilangan bulat. Dalam makalah ini, dipelajari dua kelas hipergraf yaitu, bidang Fano dan latin square orde 3. Dapat ditunjukkan bahwa kedua kelas hipergraf tersebut adalah integral. Selanjutnya, ditentukan hipergraf hasil operasi kali Kartesius dari kedua hipergraf tersebut. Dapat dibuktikan bahwa operasi kali Kartesius pada hipergraf mempertahankan sifat keintegralan.References
bibitem{C} Balinska, K. T., Cvetkovic, D., Radosavljevic, Z., Simic, S. K., dan Stevanovic, D., (2002): A survey on integral graphs, emph{Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat.}, textbf{13}, 42 –- 65.
bibitem{1} Berge, C., 1973, emph{Graphs and Hypergraphs}, North-Holland Publishing Company, Amsterdam
bibitem{2} Graham, A., 1981, emph{Kronecker Product and Matrix Calculus: with Appllications}, Ellis Horwood Limited, England
bibitem{3} Harary, F., Schwenk, A.J., 1974, Which graphs have integral spectra?, emph{Graphs and Combinatorics, Lecture Notes in Mathematics}, textbf{406} : 45 -- 51.
bibitem{4} Hellmuth, M., Ostermeier L., and Stadler, P., 2012, A Survey on Hypergraph Products, emph{Math. Comput. Sci.} textbf{6}, 1 -– 32
bibitem{5} Liu, J., Mirafzal, S.M., and Zafari A., 2021, Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum, emph{Hindawi Journal of Mathematics}, textbf{2021}, Article ID 6632206,
https://doi.org/10.1155/2021/6632206
bibitem{D} Saxena, N., Saverini, S., dan Shparlinski, I., 2007: Parameters of integral circulant graph and periodic quantum dynamics, emph{International Journal of Quantum Information}, textbf{5(3)}, 417 -– 430.
bibitem{7} Schmidt, N.O., 2016, emph{Latin squares and their applications to cryptography}, Thesis, Boise State University
bibitem{B} Sripaisan, N., 2021, emph{Algebraic degree of spectra of cayley hypergraphs} Theses and Dissertations (Chula ETD). 4773., Chulalongkorn University
bibitem{8} Stinson, D.R., 2004 emph{Combinatorial Designs: Constructions and Analysis}, Springer-Verlag New York, Inc
bibitem{9} Wang, L., 2005, emph{A survey of results on integral trees and integral graphs}, Memorandum No. 1763, University of Twente, The Netherlands, ISSN 0169-2690
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Departemen Matematika dan Sains Data FMIPA UNAND
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. This ensures that the content is freely available to all users and can be shared and adapted, provided appropriate credit is given and any adaptations are distributed under the same license.
Copyright Holder
The copyright of all articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND). This applies to all published versions, including the HTML and PDF formats of the articles.
Author Rights
While the Departemen Matematika dan Sains Data FMIPA UNAND holds the copyright for all published content, authors retain important rights under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA). This license grants authors and users the following rights:
- Reuse: Authors can reuse and distribute their work for any lawful purpose, including sharing on personal websites, institutional repositories, or in subsequent publications.
- Attribution and Adaptation: Authors and others may remix, adapt, and build upon the published work for any purpose, even commercially, as long as proper credit is given to the original authors, and any derivative works are distributed under the same CC BY-SA license.
Creative Commons License (CC BY-SA)
Under the terms of the CC BY-SA license, users are free to:
- Share: Copy and redistribute the material in any medium or format.
- Adapt: Remix, transform, and build upon the material for any purpose, even commercially.
However, the following conditions apply:
- Attribution: Users must give appropriate credit to the original author(s) and Departemen Matematika dan Sains Data FMIPA UNAND, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author or the journal.
- ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same license as the original.
For more information about the CC BY-SA license, please visit the Creative Commons website.
Third-Party Content
If authors include third-party material (such as figures, tables, or images) that is not covered by a Creative Commons license, they must obtain the necessary permissions for reuse and provide proper attribution. Authors are required to ensure that any third-party content complies with open-access licensing requirements or includes permissions for redistribution under similar terms.
Copyright and Licensing Information Display
The copyright and licensing terms will be clearly displayed on each article's landing page, as well as within the full-text versions (HTML and PDF) of all published articles.
No "All Rights Reserved"
As an open-access journal, JMUA does not use "All Rights Reserved" policies. Instead, the CC BY-SA license ensures that the works remain accessible and reusable for a wide audience while still protecting both the authors' and the copyright holder's rights.
Â
