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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 graph’s edge-connectivity and the number of orbits of its automorphism group. In this paper, we discuss the edge connectedness of graphs with two orbits of the same size, and characterize when these double-orbit graphs are...
Let G=(V(G),E(G)) be a simple connected graph and F⊂E(G). An edge set F is an m-restricted edge cut if G−F is disconnected and each component of G−F contains at least m vertices. Let λ(m)(G) be the minimum size of all m-restricted edge cuts and ξm(G)=min{|ω(U)|:|U|=m and G[U] is connected}, where ω(U) is the set of edges with exactly one end vertex in U and G[U] is the subgraph of G induced by U....
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