The connected cutset connectivity of a graph
The connected (edge-)cutset connectivity \(c\kappa\) (G) \((c\kappa_ 1(G))\) of a graph G is the minimum cardinality of a vertex (edge) cutset S of G such that the subgraph induced by S is connected. Let \(\kappa\) (G) be the vertex-connectivity of G, \(\kappa_ 1(G)\) the edge-connectivity and \(\delta\) (G) the minimal degree. The author proves existence theorems for graphs with given \(\kappa\) (G), \(c\kappa\) (G), \(\delta\) (G) as well as given \(\kappa_ 1(G)\), \(c\kappa_ 1(G)\), \(\delta\) (G) and shows that for graphs with \(c\kappa_ 1(G)\subseteq c\kappa (G)\) holds \(c\kappa_ 1(G)=\delta (G)\).
scientific article; zbMATH DE number 4047766