On 3-restricted edge connectivity of undirected binary Kautz graphs

An edge cut of a connected graph is m -restricted if its removal leaves every component having order at least m . The size of minimum m -restricted edge cuts of a graph G is called its m -restricted edge connectivity. It is known that when m ≤ 4 , networks with maximal m -restricted edge connectivity are most locally reliable. The undirected binary Kautz graph U K ( 2 , n ) is proved to be maximal 2- and 3-restricted edge connected when n ≥ 3 in this work. Furthermore, every minimum 2-restricted edge cut disconnects this graph into two components, one of which being an isolated edge.