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The WK-Recursive Network (WKRN) is a hierarchical interconnection network that is recursively defined and has excellent properties for scalable message-passing multicomputer systems. In this paper, we present efficient routing and broadcasting schemes in a WKRN. For efficient routing, we define the MP-graph between the source and destination nodes of the message. For efficient broadcasting, we define the EDHP-graph and the NDST-graph. The MP-graph can also be used for message routing in the presence of faulty nodes. Similarly, the EDHP-graph (the NDST-graph) can be used for message broadcast in the presence of faulty links (nodes). Fault-tolerant communication schemes using these graphs have the advantage that no information about the presence or location of faulty components is required. Moreover, the MP-graph and the NDSTgraph can be used under different fault models. We analyze the communication delays for message routing (broadcast) along MP-graphs (EDHP-graphs and NDST-graphs) under fault-free and faulty conditions.