On computing a conditional edge-connectivity of a graph
Information Processing Letters
Almost all Cayley graphs have diameter 2
Discrete Mathematics
On optimally-λ(3) transitive graphs
Discrete Applied Mathematics
Fault-tolerant analysis of a class of networks
Information Processing Letters
Minimally 3-restricted edge connected graphs
Discrete Applied Mathematics
λc-Optimally half vertex transitive graphs with regularity k
Information Processing Letters
On optimally-λ(3) transitive graphs
Discrete Applied Mathematics
Restricted edge connectivity of harary graphs
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
A neighborhood condition for graphs to be maximally k-restricted edge connected
Information Processing Letters
Edge fault tolerance of graphs with respect to super edge connectivity
Discrete Applied Mathematics
Optimally restricted edge connected elementary Harary graphs
Theoretical Computer Science
Vulnerability of super edge-connected networks
Theoretical Computer Science
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Let X=(V,E) be a connected regular graph. X is said to be super-edge-connected if every minimum edge cut of X is a set of edges incident with some vertex. The restricted edge connectivity λ'(X) of X is the minimum number of edges whose removal disconnects X into non-trivial components. A super-edge-connected k-regular graph is said to be optimally super-edge-connected if its restricted edge connectivity attains the maximum 2k - 2. In this paper, we define the λ'-atoms of graphs with respect to restricted edge connectivity and show that if X is a k-regular k-edge-connected graph whose λ'-atoms have size at least 3, then any two distinct λ'-atoms are disjoint. Using this property, we characterize the super-edge-connected or optimally super-edge -connected transitive graphs and Cayley graphs. In particular, we classify the optimally super-edge -connected quasiminimal Cayley graphs and Cayley graphs of diameter 2. As a consequence, we show that almost all Cayley graphs are optimally super-edge-connected.