Fault Tolerant Token Ring Embedding in Double Loop Networks

A double loop network G(n; $1, ~2) is a digraph with n nodes (0, 1, . , n 1) and 2n links of the form i + i + x1 (mod n) and i + i + s2 (mod n). A double loop network G(n; ~1, $2) is LFT if there is a Hamiltonian cycle in every G(n; ~1, ~2) e where e is any link in the network. Similarly, a double loop network G(n; ~1, ~2) is NE;T if there is a Hamiltonian cycle in every G(n; ~1, ~2) u where u is a node in the network. In this paper, we present necessary and sufficient conditions for LET and NFT double loop networks, respectively.