On computing a conditional edge-connectivity of a graph
Information Processing Letters
On restricted edge-connectivity of graphs
Discrete Mathematics
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
Optimally super-edge-connected transitive graphs
Discrete Mathematics
Graph Theory With Applications
Graph Theory With Applications
Edge fault tolerance of graphs with respect to super edge connectivity
Discrete Applied Mathematics
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Let X=(V,E) be a connected graph and S@?E.S is said to be an m-restricted edge cut if X-S is disconnected and each component of X-S contains at least m vertices. Let @l^(^m^)(X) be the minimum size of all m-restricted edge cuts, and @x"m(X)=min{@w(U): U@?V,|U|=m and X[U] is connected}, where @w(U) is the number of edges with one end in U and the other end in V@?U, X[U] is the subgraph of X induced by U. A graph X is said to be optimally-@l^(^3^) if @l^(^i^)(X)=@x"i(X)(i=1,2,3). In this paper, optimally-@l^(^3^) vertex-transitive graphs are studied. In particular, generating sets of optimally-@l^(^3^) minimal Cayley graphs are completely characterized.