Vertex Set

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).

REFERENCES:

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