A twin-free graph is a graph containing no pair of twin vertices. Equivalently, every equivalence class
under equality together with twinhood is a singleton
set.
The definition excludes both true twins and false twins. Every vertex-induced subgraph
of a cograph with at least two vertices contains twins,
so the only nonempty twin-free cograph is the singleton
graph 
.
See also
Cograph,
False Twin,
True Twin,
Twin
Vertices
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References
Brandstädt, A.; Le, V. B.; and Spinrad, J. P. Graph
Classes: A Survey. Philadelphia, PA: SIAM, 1999.
Cite this as:
Weisstein, Eric W. "Twin-Free Graph."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Twin-FreeGraph.html
Subject classifications
