On computing a conditional edge-connectivity of a graph
Information Processing Letters
Generalized Measures of Fault Tolerance with Application to N-Cube Networks
IEEE Transactions on Computers
Half-transitive group actions on finite graphs of valency 4
Journal of Combinatorial Theory Series B
On restricted edge-connectivity of graphs
Discrete Mathematics
Edge-cuts leaving components of order at least three
Discrete Mathematics
Tetravalent edge-transitive graphs of girth at most 4
Journal of Combinatorial Theory Series B
Sufficient conditions for graphs to be λ′-optimal and super-λ′
Networks - Dedicated to Leonhard Euler (1707–1783)
A complete classification of cubic symmetric graphs of girth 6
Journal of Combinatorial Theory Series B
Topological Structure and Analysis of Interconnection Networks
Topological Structure and Analysis of Interconnection Networks
Super-cyclically edge-connected regular graphs
Journal of Combinatorial Optimization
| Hi-index | 0.04 |
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 G is super restricted edge connected if G-F contains an isolated edge for every minimum restricted edge cut F of G. 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 k-regular Hamiltonian graphs with k=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.