The kk-restricted edge connectivity of undirected Kautz graphs

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