Abstract
Let q=pe ? 1(mod 4) be a prime power, and let ?(q) be the Paley graph over the finite field $${\mathbb F}_q$$ . Denote by ?(q) the subgraph of ?(q) induced on the set of non-zero squares of $${\mathbb F}_q$$ . In this paper the full automorphism group of ?(q) is determined affirming the conjecture of Brouwer [Des. Codes Cryptograph. 21, 69--76 (2000)]. The proof combines spectral and Schur ring techniques.
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