In the affine case, every symmetric graph with a complete quotient that is almost multi-covered and yields a nontrivial linear space is either an affine flag graph or one of a few sporadic graphs.
Zhou, Constructing a class of symmetric graphs, European J
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Affine flag graphs and classification of a family of symmetric graphs with complete quotients
In the affine case, every symmetric graph with a complete quotient that is almost multi-covered and yields a nontrivial linear space is either an affine flag graph or one of a few sporadic graphs.