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
Explore with Wolfram|Alpha
Cite this as:
Barile, Margherita. "Separable Graph." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SeparableGraph.html