Reliability of interconnection networks modeled by a product of graphs

The product graph GmaGp of two given graphs Gm and Gp, defined by J.C. Bermond et al. [J Combin Theory, Series B 36 (1984) 32–48] in the context of the so-called (Δ,D)-problem, is one interesting model in the design of large reliable networks. This work deals with product graphs for which we provide bounds for the connectivity parameter κ. Moreover, we state sufficient conditions that guarantee these product graphs to be maximally connected or superconnected. As a consequence, we deduce that even small networks with low reliability may lead to larger networks with high levels of fault-tolerance. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 48(3), 114–120 2006