Structure connectivity of Mycielskian graph

The structure connectivity, namely κG;H, is a parameter measuring the fault tolerance of interconnection networks by deleting given substructures. Let G and H be two graphs and H is a connected subgraph of G. Denote a set of subgraphs of G by F with each element isomorphic to H. If the graph G−F is disconnected which is obtained by removing F, then we call F an H-structural cut. The smallest cardinality among all such H-structural cuts is called the H-structural connectivity of the graph G, namely as κG;H. Furthermore, we define the conditional H-structural connectivity κcG;H under two specific constraints. This paper studies the structural connectivity and conditional structural connectivity of the Mycielskian graph μG of the graph G and gives the specific values of κμG;H and κcG;H, where H∈K1,K1,1,K1,2,⋯,K1,n−3.