Strongly regular decompositions of the complete graph
In this paper several questions about amorphic association schemes and other strongly regular decompositions of the complete graph are studied, by investigating how two commuting edge-disjoint strongly regular graphs interact. A so-called amorphic association scheme has the property that all of its graphs are strongly regular. Moreover, they are all of Latin square type, or all of negative Latin square type. It is shown that any decomposition of the complete graph into three strongly regular graphs must be an amorphic association scheme. Likewise it is proved that any decomposition of the complete graph into strongly regular graphs of (negative) Latin square type is an amorphic association scheme. Strongly regular decompositions of the complete graph consisting of four graphs are studied, and a primitive counterexample to A. V. Ivanov's conjecture which states that any association scheme consisting of strongly regular graphs only must be amorphic is found.
scientific article; zbMATH DE number 1908577