A modular decomposition tree is the rooted tree whose nodes are the strong
modules of a graph, ordered by inclusion. Its root
vertex is the full vertex set, its leaves
are the singleton sets, and the children
of a node are its maximal proper strong submodules.
An internal node is parallel when the quotient on its children is an empty graph,
series when it is a complete graph, and prime otherwise.
A cograph is characterized by having no prime nodes.
See also
Cograph,
Graph Module,
Modular Decomposition,
Strong
Module
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References
Brandstädt, A.; Le, V. B.; and Spinrad, J. P. Graph
Classes: A Survey. Philadelphia, PA: SIAM, 1999.Habib, M. and
Paul, C. "A Survey of the Algorithmic Aspects of Modular Decomposition."
Comput. Sci. Rev. 4, 41-59, 2010. https://doi.org/10.1016/j.cosrev.2010.01.001.
Cite this as:
Weisstein, Eric W. "Modular Decomposition Tree."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ModularDecompositionTree.html
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