On the Terwilliger algebra and quantum adjacency algebra of the Shrikhande graph

• Main Authors: Morales, John Vincent S., Palma, Tessie M.
• Format: text
• Published: Animo Repository 2020
• Subjects: Graph connectivity; Graph theory; Algebra; Algebraic Geometry
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/11536
• Institution: De La Salle University

Let XX denote the vertex set of the Shrikhande graph. Fix xx x . Associated with xx is the Terwilliger algebra TT T TT T T of the Shrikhande graph, a semisimple subalgebra of MatXX(C). There exists a subalgebra QQ QQ of TT that is generated by the lower- ing, flat, and raising matrices in TT . The algebra QQ is semisimple and is called the quan- tum adjacency algebra of the Shrikhande graph. Terwilliger & Zitnik (2019) investigated how QQ and TT are related for arbitrary distance­regular graphs using the notion of quasi- isomorphism between irreducible TT ­modules. Using their results, together with descrip- tion of the irreducible TT ­modules of the Shrikhande graph by Tanabe (1997), we show in this paper that for the Shrikhande graph, we have QQ Q .