Proves ex_Cay(C_{2ℓ+1}, Z_p) equals 0 when p equals 2ℓ+1 and equals 2 floor((p + 2ℓ + 1) / (2(2ℓ + 1))) otherwise, for odd prime p.
Davenport,On the addition of residue classes, Journal of the London Mathematical Societys1-10(1935), no
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Odd cycles in symmetric Cayley graphs on prime cyclic groups
Proves ex_Cay(C_{2ℓ+1}, Z_p) equals 0 when p equals 2ℓ+1 and equals 2 floor((p + 2ℓ + 1) / (2(2ℓ + 1))) otherwise, for odd prime p.