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# Quasiseparable Graph

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.

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.

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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