The growing size of the multiprocessor system increases its vulnerability to component failures. It is crucial to locate and to replace the faulty processors to maintain a system’s high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. In this paper, we show that the largest connected component of the survival graph contains almost all...

We study the Optimal Linear Arrangement (OLA) problem of Halin graphs, one of the simplest classes of non-outerplanar graphs. We present several properties of OLA of general Halin graphs. We prove a lower bound on the cost of OLA of any Halin graph, and define classes of Halin graphs for which the cost of OLA matches this lower bound. We show for these classes of Halin graphs, OLA can be comput...