A conditional edge connectivity of double-orbit networks

The edge connectivity is a kind of classic measure of fault tolerance of networks. It is well known that the edge-connectivity of a simple, connected, vertex transitive graph attains its regular degree. It is then natural to consider the relationship between the edge connectivity and the number of orbits of its automorphism group. The double-orbit graphs with two orbits of the same size is a generalization of vertex transitive networks, which contains several classic network models. In this note, we obtain a sufficient condition for such double-orbit graphs to be super-λ′.