A subset of vertices X is said to be a cutset if G− X is not connected. A cutset X is called an
Rg-cutset if every component of G− X has at least g+ 1 vertices. If G has at least one Rg …

Reliability evaluation of interconnection network is important to the design and maintenance
of multiprocessor systems. The h-extra connectivity κ h (G) is an important subject for a …

For a graph G=(V, E), a subset F⊆ V (G) is called an Rk-vertex-cut of G if G− F is
disconnected and each vertex u∈ V (G)− F has at least k neighbors in G− F. The Rk-vertex …

Given a connected graph G and an integer 1≤ p≤⌊| V (G)|/2⌋, a p-restricted edge-cut of G
is any set of edges S⊂ E (G), if any, such that G− S is not connected and each component of …

For a strongly connected digraph D the restricted arc‐connectivity λ′(D) is defined as the
minimum cardinality of an arc‐cut over all arc‐cuts S satisfying that D‐S has a non‐trivial …

An edge cut W of a connected graph G is a k-restricted edge cut if G− W is disconnected,
and every component of G− W has at least k vertices. The k-restricted edge connectivity is …

For a strongly connected digraph D the restricted arc-connectivity λ′(D) is defined as the
minimum cardinality of an arc-cut over all arc-cuts S satisfying that DS has a non-trivial …

A digraph D is cycle separable if it contains two vertex disjoint directed cycles. For a cycle
separating digraph D, an arc set S is a cycle separating arc-cut if D− S has at least two …

An edge cut X of a connected graph G is a k-restricted edge cut if GX is disconnected and
every component of GX has at least k vertices. Additionally, if the deletion of a minimum k …

The k-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), an important …