An edge cut (Holton and Sheehan 1993, p. 14; West 2000, p. 152), edge cut set, edge cutset (Holton and Sheehan 1993, p. 14), or sometimes simply "cut
set" or "cutset" (e.g., Harary 1994, p. 38) of a connected
graph , is a set of edges of which, if removed (or "cut"), disconnects
the graph (i.e., forms a disconnected graph ).
An edge cut set of size 1 corresponds to a graph bridge .
The size of a minimum edge cut in a connected graph edge connectivity
An edge cut set of smallest size in a given connected graph Wolfram
Language using the function FindEdgeCut g ].
For a not-necessarily-connected graph edge set connected components
than
See also Cyclic Edge Connectivity ,
Disconnected Graph ,
Edge
Connectivity ,
Graph Bridge ,
Minimum
Edge Cut ,
Vertex Cut
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References Gross, J. T. and Yellen, J. Graph Theory and Its Applications, 2nd ed. Harary,
F. Graph
Theory. Holton,
D. A. and Sheehan, J. The
Petersen Graph. Skiena, S. "Reconstructing Graphs from Cut-Set Sizes."
Info. Proc. Lett. 32 , 123-127, 1989. Skiena, S. Implementing
Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. West, D. B. Introduction
to Graph Theory, 2nd ed.
Cite this as:
Weisstein, Eric W. "Edge Cut." From MathWorld https://mathworld.wolfram.com/EdgeCut.html
Subject classifications
gives the edge connectivity 
.
can be found in the Wolfram
Language using the function FindEdgeCut[g].
, an edge cut is an edge set 
such that 
has more connected components
than 
(Gross and Yellen 2006, p. 81).
