Please use H_n+1 in induction thanks

Prove that He has a Hamiltonian cycle for all n > 2. Hint: use induction. The Hamming cube of dimension n is the undirected graph Hn = (Vn, En) where Vn = {w: w is a binary string of length n} and En = {(v, w): v and w differ in exactly one digit). Prove that He has a Hamiltonian cycle for all n > 2. Hint: use induction. The Hamming cube of dimension n is the undirected graph Hn = (Vn, En) where Vn = {w: w is a binary string of length n} and En = {(v, w): v and w differ in exactly one digit)