The n-dimensional hypercube is the graph with 2n nodes labelled 0,1,...,2’n-1 and an edge joining two nodes whenever their binary representation differs in a single coordinate. The problem of deciding whether a given graph is a subgraph of an n-dimensional cube has recently been shown to be NP-complete. In this paper the authors illustrate a reduction technique used to obtain NP-completeness results for a variety of hypercube related graphs. They consider the subgraph isomorphism problem on two related families of graphs, the dilation two hypercubes and generalized hypercubes. The authors show that the embedding problem for both of these families is NP-complete.
