Orthogonal projection and liftings of Hamilton-decomposable Cayley graphs on abelian groups

In this article we introduce the concept of ( p , α ) -switching trees and use it to provide sufficient conditions on the abelian groups G and H for when Cay  ( G × H ; S ∪ B ) is Hamilton-decomposable, given that Cay  ( G ; S ) is Hamilton-decomposable and B is a basis for H . Applications of this result to elementary abelian groups and Paley graphs are given.