The vertex set of a graph is simply a set of all vertices of the graph. The cardinality of the vertex set for a given graph is known as the vertex count of .

The vertex set for a particular graph embedding of a graph is given in the Wolfram Language using PropertyValue[g, VertexCoordinates] or GraphEmbedding[g]. Vertex sets for many named graphs are available via GraphData[graph, "VertexCoordinates"] (for the primary embedding) and GraphData[graph, "Embeddings"] (for all available embeddings).

The vertex set of an abstract simplicial complex is the union of one-point elements of (Munkres 1993, p. 15).

See also

Arc Set, Domination Number, Edge Set, Vertex Count, Vertex Scheme

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References

Munkres, J. R. Elements of Algebraic Topology. New York: Perseus Books Pub., 1993.

Referenced on Wolfram|Alpha

Vertex Set

Cite this as:

Weisstein, Eric W. "Vertex Set." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VertexSet.html

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