A study of odd graphs as fault-tolerant interconnection networks

Odd graphs are analyzed to determine their suitable in designing interconnection networks. These networks are shown to possess many features that make them competitive with other architectures, such as ring, star, mesh, the binary n-cube and its generalized form, the chordal ring, and flip-trees. Among the features are small internode distances, a lighter density, simplicity in implementing various self-routing algorithms (both for faulty and nonfaulty networks), capability of maximal fault tolerance, strong resilience, and good persistence. The routing algorithms (both for the faulty and fault-free networks) do not require any table lookup mechanism, and intermediate nodes do not need to modify the message. These graphs are shown to have a partitioning property that is based on Hadamard matrices and can be effectively used for a system´s expansion and self-diagnostics