Abstract
Let G=(V, E) be a multigraph. The multigraph G is called maximally edge-connected if λ(G)=δ(G), and super edge-connected if every minimum edge-cut is a set of edges incident with some vertex. The restricted edge-connectivity 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. This work characterizes maximally edge-connected vertex-transitive multigraphs, super edge-connected vertex-transitive multigraphs, and λ′-optimal vertex-transitive multigraphs.
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