Decomposing the Higman-Sims Graph into Double Petersen Graphs

It has been known for some time that the Higman-Sims graph can be decomposed into the disjoint union of two Hoffman-Singleton graphs. In this paper, we establish that the Higman-Sims graph can be edge decomposed into the disjoint union of 5 double-Petersen graphs, each on 20 vertices. It is shown that, in fact, this can be achieved in 36,960 distinct ways. It is also shown that these different ways fall into a single orbit under the automorphism group \(\text{HS}\) of the graph.