| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 421234 | Discrete Applied Mathematics | 2012 | 5 Pages |
An edge cut of a connected graph is called restricted if it separates this graph into components each having order at least 2; a graph GG is super restricted edge connected if G−FG−F contains an isolated edge for every minimum restricted edge cut FF of GG. It is proved in this paper that a connected regular edge-transitive graph of valency at least 3 is not super restricted edge connected if and only if it is either the three dimensional hypercube, or a tetravalent edge-transitive graph of girth 3 and of order at least 6. As a result, there are infinitely many kk-regular Hamiltonian graphs with k≥3k≥3 which are not super restricted edge connected. This answers negatively a question in [J. Ou, F. Zhang, Super restricted edge connectivity of regular graphs, Graphs & Combin. 21 (2005) 459–467] regarding the relationship between restricted edge connected graphs and Hamiltonian graphs.
