Hamiltonian-connectedness of the WK-recursive network

Recently, the WK-recursive network has received much attention due to its many favorable properties such as a high degree of regularity, scalability, and symmetry. In this paper, using the recursive construction method, we show that the WK-recursive network is Hamiltonian-connected. A network is Hamiltonian-connected if it contains a Hamiltonian path between every two distinct nodes. In other words, a Hamiltonian-connected network can embed the longest linear array between any two distinct nodes with dilation, congestion, load, and expansion all equal to one.