Terwilliger algebras of complete multipartite graphs

Document Type : Original Paper

Authors

Department of Mathematics, Bojnourd Branch, Islamic Azad University, Bojnourd, Iran

Abstract

Let $\Gamma=K_{p_1,...,p_r}$ be complete multipartite graph and $ x_0 $ be a fix vertex. Let $ T $ be Terwilliger algebra of $ \Gamma $ with base point $ x_0 $. In this paper, we study the modular structure of this algebra and it will be shown that up to isomorphism there are either $ s+2 $ or $ s+3 $ irreducible modules in which $ s $ is the number of distinct numbers in $ {p_1,...,p_r} $. Along with other results, the dimensions of these modules will be computed as complex vector spaces.

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References

[1] P. Terwilliger, The subconstituent algebra of an association scheme I, J. Algebraic Comb., 1 (1992),363–388.
[2] P. Terwilliger, The subconstituent algebra of an association scheme II, J. Algebraic Comb., 2 (1993)73–103.
[3] P. Terwilliger, The subconstituent algebra of an association scheme III, J. Algebraic Comb., 3 (1993)177–210.
[4] P. Terwilliger, Algebraic Graph Theory, unpublished lecture notes taken by H.Suzuki.
[5] P. Terwilliger, Arjana Zitnik, The quantum adjacency algebra and subconstituent algebra of a graph,J. Comb. Theory, Ser. A 166 (2019) 297–314.
Journal of Advanced Mathematical Modeling
Volume 12, Issue 3
November 2022
Pages 428-436

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History

  • Receive Date: 15 April 2022
  • Revise Date: 14 October 2022
  • Accept Date: 23 October 2022

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