On the Exceptional Case in a Characterization of the Arcs of a Complete Graph

It is known that a certain simple set of properties characterize the relationship of adjacency of the n(n − 1)/2 arcs of the complete graph of order n, when n ≠ 8, and that these properties are not a sufficient characterization when n = 8 (see [1], [2], [3], [4], and [7]). The present paper describes a method for enumerating all counter-examples when n = 8.