Vulnerability analysis of group divisible generalized petersen graphs

An interconnection network can be modeled by a graph where processors correspond to vertices and communication links correspond to edges. In a network consisting of multiple processors, some processors may fail, which can negatively impact the overall system's reliability and performance. Therefore, measuring the network's resilience against failure is critical for ensuring effective design and maintenance. Connectivity and edge connectivity are important metrics that determine reliability and vulnerability of a network. Additionally, other metrics, such as super (edge) connectivity, have also been defined. However, in most of these metrics, it is assumed that all neighbors of any vertex or all vertices connected to any edge can fail simultaneously. In reality, adjacent vertices could affect each other, which means that the neighbors of a faulty vertex are more likely to fail than other vertices. In 2016, Lin et al. introduced the concepts of structure connectivity and substructure connectivity to measure connectivity for specific graph structures, aiming to optimize the vulnerability parameters of networks. In this thesis, a vulnerability analysis of the group divisible generalized Petersen graphs, a family of 3-regular graphs, is conducted. In this context, the connectivity, edge connectivity, super connectivity, super edge connectivity, structure connectivity, and substructure connectivity of group divisible generalized Petersen graphs are examined.