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True Twin

True twins are distinct adjacent vertices of a graph that have the same closed neighborhood. Thus u and v are true twins when N[u]=N[v].

True twins are also called coduplicate vertices. Each equivalence class of true twins induces a complete graph and is a graph module.

See also

False Twin, Graph Module, Graph Neighborhood, Twin Vertices

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References

Brandstadt, A.; Le, V. B.; and Spinrad, J. P. Graph Classes: A Survey. Philadelphia, PA: SIAM, 1999.Klavžar, S.; Kuziak, D.; and Yero, I. G. "Further Contributions on the Outer Multiset Dimension of Graphs." Results Math. 78, Paper 50, 2023. https://doi.org/10.1007/s00025-022-01829-8.

Cite this as:

Weisstein, Eric W. "True Twin." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrueTwin.html

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