Vertex Set (original) (raw)
Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology
Alphabetical Index New in MathWorld
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
Explore with Wolfram|Alpha
References
Munkres, J. R. Elements of Algebraic Topology. New York: Perseus Books Pub., 1993.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Vertex Set." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VertexSet.html