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The connectivity of a graph is an important parameter to measure itsreliability. Structure and substructure connectivity, component connectivityand $k$-restricted connectivity are well-known generalizations of the conceptof connectivity, which have been extensively studied from the combinatorialpoint of view. Very little result is known about their complexity other thanthe recently obtained computational complexity of $k$-restrictededge-connectivity. In this paper, we zero in on characterizing the complexityof structure and substructure connectivity, component connectivity and$k$-restricted connectivity of graphs, showing that they are all NP-complete.

On complexity of structure and substructure connectivity, component connectivity and restricted connectivity of graphs