آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 125 |
| تعداد مقالات | 1,580 |
| تعداد مشاهده مقاله | 1,733,025 |
| تعداد دریافت فایل اصل مقاله | 1,611,575 |
Algorithm for describing the Terwilliger and quantum adjacency algebras of a distance-regular graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 15، دوره 11، شماره 3، آذر 2026، صفحه 975-984 اصل مقاله (386.69 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29114.1874 | ||
| نویسندگان | ||
| Abdillah Ahmad* 1؛ John Vincent Morales2؛ Pritta Etriana Putri3 | ||
| 1Master Program in Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia | ||
| 2Department of Mathematics and Statistics, De La Salle University, Manila, Philippines | ||
| 3Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia | ||
| چکیده | ||
| In this paper we consider an algorithm for determining a basis for the Terwilliger and quantum adjacency algebras of a distance-regular graph. For the Terwilliger algebra, we consider the generating set. For the quantum adjacency algebra, we consider the generating set consisting of the raising, flat, and lowering matrices. We give optimization method by using generating matrices with a block-matrix structure so that the number of matrix multiplications required is reduced. | ||
| کلیدواژهها | ||
| distance-regular graphs؛ Terwilliger algebra؛ subconstituent algebra؛ quantum decomposition؛ algorithm optimization | ||
| مراجع | ||
|
[1] J. Alman and V.V. Williams, A refined laser method and faster matrix multiplication, Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA) (D. Marx, ed.), SIAM, 2024, pp. 522 – 539. https://doi.org/10.1137/1.9781611976465.32
[2] E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin/Cummings, 1984.
[3] B. Fernández and Š. Miklavič, On the terwilliger algebra of distance-biregular graphs, Linear Algebra Appl. 597 (2020), 18–32. https://doi.org/10.1016/j.laa.2020.03.016
[4] B. Fernández and Š. Miklavič, On bipartite graphs with exactly one irreducible T-module with endpoint 1, which is thin, European J. Combin. 97 (2021), 103387. https://doi.org/10.1016/j.ejc.2021.103387
[5] J.M. Goethals and J.J. Seidel, Strongly regular graphs derived from combinatorial designs, Canad. J. Math. 22 (1970), no. 3, 597–614. https://doi.org/10.4153/CJM-1970-067-9
[6] A. Hanaki and M. Yoshikawa, Terwilliger algebras and some related algebras defined by finite connected simple graphs, Discrete Math. 346 (2023), no. 9, 113509. https://doi.org/10.1016/j.disc.2023.113509
[7] A. Hora and N. Obata, Quantum Probability and Spectral Analysis of Graphs, Springer, Berlin, 2007.
[8] S.D. Li, Y.Z. Fan, T. Ito, M. Karimi, and J. Xu, The isomorphism problem of trees from the viewpoint of terwilliger algebras, J. Combin. Theory Ser. A 177 (2021), 105328. https://doi.org/10.1016/j.jcta.2020.105328
[9] Y. Tan, Y. Zhang, T. Xia, and X. Liang, Terwilliger algebras of a fan graph, Journal of Hefei University of Technology Natural Science Edition 46 (2023), no. 3, 419–425.
[10] P. Terwilliger, The subconstituent algebra of an association scheme,(part I), J. Algebraic Combin. 1 (1992), no. 4, 363–388. https://doi.org/10.1023/A:1022494701663
[11] P. Terwilliger and A. Žitnik, The quantum adjacency algebra and subconstituent algebra of a graph, J. Combin. Theory Ser. A 166 (2019), 297–314. https://doi.org/10.1016/j.jcta.2019.02.022
[12] J. Xu, T. Ito, and S.D. Li, Irreducible representations of the Terwilliger algebra of a tree, Graphs Combin. 37 (2021), no. 5, 1749–1773. https://doi.org/10.1007/s00373-021-02384-9 | ||
|
آمار تعداد مشاهده مقاله: 267 تعداد دریافت فایل اصل مقاله: 312 |
||