Open Graph Neighborhood

The open graph neighborhood of a graph vertex in a graph is the set

consisting of the vertices adjacent to , but not itself. Adding gives the closed neighborhood .

Two nonadjacent vertices are false twins exactly when their open graph neighborhoods are equal.

See also

Closed Neighborhood, False Twin, Graph Neighborhood, 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. "Open Graph Neighborhood." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OpenGraphNeighborhood.html

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