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In this paper, we prove the existence of directed strongly regular graphs with parameters (63, 11, 8, 1, 2). We show that there are exactly two non-isomorphic directed strongly regular graphs with parameters (63, 11, 8, 1, 2) on which PSL (2, 8) acts as and automorphism group, transitively on the vertices of the digraphs. Both directed strongly regular graphs have PSL (2, 8): Z₃ as the full automorphism group.
Crnković et al. (Wed,) studied this question.
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