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).