Distance regular covers of complete graphs from Latin squares
We describe a new construction of distance regular covers of a complete graph K-q(2t) With fibres of size q(2t-1), q a power of 2. When q = 2, the construction coincides with the one found in [D. de Caen, R. Mathon, G.E. Moorhouse. J. Algeb. Combinatorics, Vol. 4 (1995) 317] and studied in [T. Bending, D. Fon-Der-Flaass, Elect. J Combinatorics, Vol. 5 (1998) R34]. The construction uses, as one ingredient, an arbitrary symmetric Latin square of order q; so, for large q, it can produce many different covers.
distance regular covers latin squares distance regular graphs