A graph 
is said to be separable if it is either disconnected
or can be disconnected by removing one vertex, called articulation.
A graph that is not separable is said to be biconnected
(or nonseparable).
Separable Graph
See also
Articulation Vertex, Biconnected Graph, Quasiseparable GraphThis entry contributed by Margherita Barile
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Cite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Separable Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SeparableGraph.html