On Edge Cut of Graphs Leaving Components of Order at Least Five

An edge cut of a connected graph is 5-restricted if its removal leaves every component having order at least five. Graphs that contain 5-restricted edge cuts are characterized in this paper. As a result, it is shown that a connected graph G of order at least 13 contains 5-restricted edge cuts if and only if $${G \setminus v}$$ contains a component of order at least five for every vertex v of graph G.