Permutation Graphs and Transitive Graphs

A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if each minimum vertex cut creates exactly two components, one of which is an isolated vertex. It is proved that a connected ...

A graph G is said to be super-connected if any minimum cut of G isolates a vertex. In a previous work due to the second author of this note, super-connected graphs which are both vertex transitive and edge transitive are characterized. In this note, we ...

Let X=(V,E) be a connected regular graph. X is said to be super-edge-connected if every minimum edge cut of X is a set of edges incident with some vertex. The restricted edge connectivity λ'(X) of X is the minimum number of edges whose removal ...