Minimum layout of hypercubes and folded hypercubes into the prism over caterpillars

The problem of embedding an n-node graph G into an n-node graph H is an important aspect in parallel and distributed processing. Graph embedding results have been successfully used to establish equivalence of interconnections in parallel and distributed machines. The binary hypercube is one of the most widely used multiprocessor systems due to its simple, deadlock-free routing and broadcasting properties. The folded hypercube is an important variant of hypercube with the same number of nodes. Trees are the fundamental graph theoretical models in many fields including artificial intelligence and various network designs. In this paper, we consider the problem of embedding the hypercube and folded hypercube into the prism over a caterpillar in such a way as to minimise its layout.