version ISSN 0719-0646
The point graph of a generalized quadrangle GQ (s, t) is a strongly regular graph G = srg( ?, ?, ?, μ) whose parameters depend on s and t. By a detailed analysis of the adjacency matrix we compute the Terwilliger algebra of this kind of graphs (and denoted it by T ). We find that there are only two non-isomorphic Terwilliger algebras for all the generalized quadrangles. The two classes correspond to wether s2 = t or not. We decompose the algebra into direct sum of simple ideals. Considering the action ? × Cx→ Cx we find the decomposition into irreducible T -submodules of Cx (where X is the set of vertices of the G ).
Keywords : strongly regular graphs; neralized quadrangles; Terwilliger algebra.