Generating Two-Transitive Equidistance Spaces
Two-transitive equidistance spaces can be represented as edge colorings of complete graphs with the property that any two vertices can be mapped to any other two vertices while preserving the structure of the coloring. This paper begins by disproving the conjecture that a two-transitive equidistance space with fewer colors than points must be regular, using a design based on cosets. The idea of generating an equidistance space from a given group of automorphisms and set of edges is then discussed, and a theorem which guarantees the existence of two-transitive generated designs is proven. The relationships among equidistance subrelations are then explored, including a theorem which states that the two-transitive subrelations form a lattice.
Isaac, Catherine R., "Generating Two-Transitive Equidistance Spaces" (1998). Honors Theses. 664.