Abstract
Let G be a connected graph. The graph G is said to be super-connected if for every minimum vertex cut S of G, G−S has isolated vertices. Moreover, it is said to be hyper-connected if for every minimum vertex cut S, G−S has exactly two components, one of which is an isolated vertex. In this note, we give a necessary and sufficient condition for a graph G whose jump graph J(G) (the complement of line graph of G) is, respectively, super-connected and hyper-connected.
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