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 g is known as the vertex count of g. The vertex set for a particular graph embedding of a graph g 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 V of an abstract simplicial complex S is the union of one-point elements of S.

arc set | domination number | edge set | vertex count | vertex scheme