On restricted edge-connectivity of half-transitive multigraphs

Let G = (V,E) be a multigraph (it has multiple edges, but no loops). We call G maximally edge-connected if λ(G) = δ(G), and G super edge-connected if every minimum edge-cut is a set of edges incident with some vertex. The restricted edgeconnectivity λ′(G) of G is the minimum number of edges whose removal disconnects G into non-trivial components. If λ′(G) achieves the upper bound of restricted edge-connectivity, then G is said to be λ′-optimal. A bipartite multigraph is said to be half-transitive if its automorphism group is transitive on the sets of its bipartition. In this paper, we will characterize maximally edge-connected half-transitive multigraphs, super edge-connected half-transitive multigraphs, and λ′-optimal half-transitive multigraphs.