Abstract
Let [Formula: see text], [Formula: see text] be the set of all [Formula: see text] matrices over a finite field [Formula: see text], and [Formula: see text] the subset of [Formula: see text] consisting of all rank one matrices. In this paper, we first determine the automorphism group and the fixing number of the orthogonality graph of [Formula: see text], and then characterize the automorphism group and the fixing number of the orthogonality graph of [Formula: see text].
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