Let A be an edge cut of a connected graph G. Then the cyclic edge connectivity λ_c(G) is the size of a smallest cyclic edge cut, i.e., a smallest edge cut A such that G - A has two connected components, each of which contains at least one graph cycle. Cyclic edge connectivity was considered as early as 1880 by Tait. Note that Grünbaum and others use the term "cyclically k-connected" (omitting in the word "edge") to refer to a graph that cannot be broken into two separate parts each of which contain a cycle by an edge cut of fewer than k edges.

edge connectivity | edge cut | snark