Abstract
This chapter reviews two graphs, phrased switching classes of graphs, sets of equidistant points in elliptic geometry, sets of equiangular lines in Euclidean geometry, binary maps of triples with vanishing co-boundary, and double coverings of complete graphs. A graph (Ω, E) is defined by its vertex set Ω and its edge set E, which is a subset of the set Ω of the unordered pairs of elements from Ω. For any ω Δ Ω, the triple set Δ of any two-graph (Ω, Δ) is determined by its triples containing ω. There is a one-to-one correspondence between the two-graphs and the switching classes of graphs on the set of n elements. A set of lines in Euclidean r-space is a set of equiangular lines whenever each pair of lines has the same angle. A two-graph (Ω, Δ) is regular whenever each pair of elements of n is contained in the same number a of triples of Δ.
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