Certain graphs with exactly one irreducible $T$-module with endpoint $1$, which is thin: the pseudo-distance-regularized case

Blas Fernández

Let $\Gamma$ denote a finite, simple and connected graph. Fix a vertex $x$ of $\Gamma$ which is not a leaf and let $T=T(x)$ denote the Terwilliger algebra of $\Gamma$ with respect to $x$. Assume…