The Effect of Node Failures in Substar Reliability of a Star Network- a Combinatorial Approach

Abstract

The star graph is a hierarchical graph, and rich in containing substars (or graphs with smaller size but with the same topological properties as the original). Given a set of faulty nodes, we determine the ability to recover substars of a given dimension from the original network. A study of the number of faulty nodes that are required to damage every subnetwork of a given size is also presented.