Connectivity and structure connectivity in Goldberg snark

A network is modeled as a simple connected graph. The reliability and fault tolerance of a network are important indicators for evaluating its performance. One of performance indicators of a network is the connectivity parameter. However, this parameter only considers the failure of a single vertex and assumes that all its neighbors fail simultaneously. Therefore, it ignores structural faults of a network. Due to these shortcomings, various connectivity parameters such as super connectivity, structure-connectivity, and substructure-connectivity have been defined. The connectivity (respectively, edge connectivity) is the minimum number of vertices (respectively, edges) to delete to make the graph disconnected or isomorphic to a single isolated vertex. The super connectivity (respectively, super edge connectivity) is the minimum number of vertices (respectively, edges) to delete to make the graph disconnected without isolated vertices. Let G be a connected graph and H be a subgraph of G. The H-structure connectivity (respectively, H-substructure connectivity) of G is the minimum cardinality of a set of connected subgraphs in G, whose removal disconnects G and each element in the set is isomorphic to H (respectively, a connected subgraph of H). In this thesis, connectivity, edge connectivity, super connectivity, super edge connectivity, structure connectivity and substructure connectivity parameters are examined on the Goldberg snark, which is a cubic graph. connectivity.