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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