Abstract :
An edge cut of a connected graph is 4-restricted if it disconnects this graph with each component having order at least four. The size of minimum 4-restricted edge cuts of graph G is called its 4-restricted edge connectivity and is denoted by image. Let image, where image denotes the number of edges of graph G with exactly one endpoint in F. For connected graphs that contain 4-restricted edge cuts, image is proved to be an upper bound on image if G has order at least 11. If G is a k-regular vertex-transitive graph of girth at least five, then image when image.
