Super connectivity of line graphs
Information Processing Letters
On reliability of the folded hypercubes
Information Sciences: an International Journal
Fault-tolerant analysis of a class of networks
Information Processing Letters
Restricted arc-connectivity of digraphs
Information Processing Letters
Diameter-sufficient conditions for a graph to be super-restricted connected
Discrete Applied Mathematics
Super connectivity of line graphs
Information Processing Letters
Edge fault tolerance of super edge connectivity for three families of interconnection networks
Information Sciences: an International Journal
λ'-Optimality of Bipartite Digraphs
Information Processing Letters
The k-restricted edge-connectivity of a product of graphs
Discrete Applied Mathematics
On the connectivity and restricted edge-connectivity of 3-arc graphs
Discrete Applied Mathematics
Vulnerability of super edge-connected networks
Theoretical Computer Science
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The restricted-edge-connectivity of a graph G, denoted by λ′(G), is defined as the minimum cardinality over all edge-cuts S of G, where G-S contains no isolated vertices. The graph G is called λ′-optimal, if λ′(G) = ξ(G), where ξ(G) is the minimum edge-degree in G. A graph is super-edge-connected, if every minimum edge-cut consists of edges adjacent to a vertex of minimum degree. In this paper, we present sufficient conditions for arbitrary, triangle-free, and bipartite graphs to be λ′-optimal, as well as conditions depending on the clique number. These conditions imply super-edge-connectivity, if δ (G) ≥ 3, and the equality of edge-connectivity and minimum degree. Different examples will show that these conditions are best possible and independent of other results in this area. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 228–246, 2005