Abstract
In this paper, we investigate the existence of two self-orthogonal Latin squares of order v (2- SOLS ( v ) ). It is found that 2- SOLS ( v ) exist for all v ≥ 7 except possibly for v ∈ { 10 , 12 , 14 , 18 , 21 , 22 , 24 , 30 , 34 } . A number of sets of 2 incomplete SOLS (2 ISOLS) (and hence also 4 incomplete mutually orthogonal Latin squares, briefly 4 IMOLS) are also given.
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