The -restricted edge connectivity of undirected Kautz graphs

The k -restricted edge connectivity is a more refined network reliability index than edge connectivity. In this paper, we study the undirected Kautz graph U K ( d , n ) , an important model of networks, give an upper bound on the k -restricted edge connectivity of U K ( d , n ) for some small k and determine the 4-restricted edge connectivity of U K ( 2 , n ) .