Reliability analysis with structure connectivity in a hypercube variant

One of the main problems in a communication network is the continuity of data flow. Modeling with graph theory is a common method for addressing problems in communication networks used in various applications. It is an important problem to determine the state of communication in the remaining network when damage occurs in any center on the network or in the connections between the centers. These measurements must be conducted in advance to determine an effective network topology. For this purpose, several vulnerability parameters have been defined on graphs. Connectivity is one of the oldest vulnerability parameters; it determines the minimum number of vertices whose deletion results in a disconnected graph. However, in the definition of connectivity, it is assumed that all the neighbors of any vertex can be damaged at the same time, and this analysis cannot yield favorable results. In the literature, there are several vulnerability parameters defined to compensate for this deficiency. On the other hand, most studies on network vulnerability so far have assumed that vertices are damaged independently of their neighborhoods. However, in many real-world problems, the neighbors of a damaged vertex will be more vulnerable, or, more likely to be damaged. In 2016, Lin et al. proposed the structure connectivity, to consider the cases where each component of the damage has a specific structure or is a substructure of a specific structure. In this thesis, we addressed a regular infinite graph class, namely folded divide-and-swap cubes and investigated this class in terms of structure and substructure connectivity.