An unusual decomposition of a complete 7-partite graph of order 28 (Q941404)

The authors present a decomposition of the 24-regular complete 7-partite graph into two non-isomorphic 12-regular graphs, both of which are vertex-transitive, arc-transitive, one with a large primitive automorphism group and the other with a small imprimitive automorphism group. They point out some interesting properties of decompositions of complete regular \(n\)-partite graphs into two subgraphs concerning automorphism groups of the subgraphs and pose two problems related to those properties.