Topological properties of incomplete WK-recursive networks

WK-recursive networks, which were originally proposed by Vecchia and Sanges (1988), have suffered from the rigorous restriction of the number of nodes. Like other incomplete networks, incomplete WK-recursive networks are proposed to relieve this restriction. It is first shown that the structures of the incomplete WK-recursive networks are conveniently represented with multistage graphs. This representation can provide a uniform look at the incomplete WK-recursive networks. Using this they: (1) compute the connectivities of the incomplete WK-recursive networks; (2) show that they are Hamiltonian if their connectivities are greater than one; and (3) propose a sufficient and necessary condition for a Hamiltonian path in an incomplete WK-recursive network with connectivity 1