A linear time algorithm for embedding hypercube into cylinder and torus

In this paper we solve two conjectures proposed by Manuel et al. (2011) [7] to obtain exact wirelength of embedding an r  -dimensional hypercube into cylinder C2r1×P2r2C2r1×P2r2 and torus C2r1×C2r2C2r1×C2r2, where r1+r2=rr1+r2=r and r1≤r2r1≤r2. We provide a linear time algorithm to compute the exact wirelength of embedding hypercube into cylinder and torus. Further we extend the result for higher dimensional cylinder and torus.