A graph that becomes disconnected when removing a suitable complete subgraph , called a vertex cut, is said to be quasiseparable. The two simplest cases are those where is the null graph (which means that is disconnected) or is the singleton graph (which means that can be disconnected by removing one vertex, called articulation or cut vertex). Under these circumstances, is called separable. A forest is always separable, since every vertex of degree at least two is an articulation vertex.

# Quasiseparable Graph

## See also

Articulation Vertex, Biconnected Graph, Separable Graph, Vertex Cut
*This entry contributed by Margherita
Barile*

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## References

Balakrishnan, R. and Ranganathan, K. "Vertex Cuts and Edge Cuts." §3.1 in*A Textbook of Graph Theory.*New York:Springer-Verlag, pp. 44-48, 1999.Biggs, N.

*Algebraic Graph Theory, 2nd ed.*Cambridge, England: Cambridge University Press, p. 67, 1993.

## Referenced on Wolfram|Alpha

Quasiseparable Graph## Cite this as:

Barile, Margherita. "Quasiseparable Graph." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/QuasiseparableGraph.html