On weakly symmetric graphs of order twice a prime
Journal of Combinatorial Theory Series B
On computing a conditional edge-connectivity of a graph
Information Processing Letters
On the 2-extendability of planar graphs
Discrete Mathematics
Lower bound of cyclic edge connectivity for n-extendability of regular graphs
Discrete Mathematics
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Conditional Connectivity Measures for Large Multiprocessor Systems
IEEE Transactions on Computers
A census of semisymmetric cubic graphs on up to 768 vertices
Journal of Algebraic Combinatorics: An International Journal
Tetravalent edge-transitive graphs of girth at most 4
Journal of Combinatorial Theory Series B
Cubic symmetric graphs of order a small number times a prime or a prime square
Journal of Combinatorial Theory Series B
Infinitely Many Hypohamiltonian Cubic Graphs of Girth 7
Graphs and Combinatorics
Super cyclically edge connected transitive graphs
Journal of Combinatorial Optimization
Super restricted edge connectivity of regular edge-transitive graphs
Discrete Applied Mathematics
| Hi-index | 0.00 |
A cyclic edge-cut of a graph G is an edge set, the removal of which separates two cycles. If G has a cyclic edge-cut, then it is called cyclically separable. We call a cyclically separable graph super cyclically edge-connected, in short, super-驴 c , if the removal of any minimum cyclic edge-cut results in a component which is a shortest cycle. In Z. Zhang, B. Wang (Super cyclically edge-connected transitive graphs, J. Combin. Optim. 22:549---562, 2011), it is proved that a connected edge-transitive graph is super-驴 c if either G is cubic with girth at least 7 or G has minimum degree at least 4 and girth at least 6, and the authors also conjectured that a connected graph which is both vertex-transitive and edge-transitive is always super cyclically edge-connected.In this article, for a 驴 c -optimal but not super-驴 c graph G, all possible 驴 c -superatoms of G which have non-empty intersection with other 驴 c -superatoms are determined. This is then used to give a complete classification of non-super-驴 c edge-transitive k(k驴3)-regular graphs.