VertexColor is an option that allows the user to associate colors with vertices.

VertexConnectivityGraph[g] returns a directed graph that contains an edge corresponding to each vertex in g and in which edge-disjoint paths correspond to vertex-disjoint ...

VertexCoverQ[g, c] yields True if the vertices in list c define a vertex cover of graph g.

VertexLabelColor is an option that allows the user to associate different colors to vertex labels.

VertexLabelPosition is an option that allows the user to place a vertex label in a certain position relative to the vertex.

VertexNumberColor is an option that can be used in ShowGraph to associate different colors to vertex numbers.

VertexWeight is an option that allows the user to associate weights with vertices.

V[g] gives the order or number of vertices of the graph g.

WeaklyConnectedComponents[g] gives the weakly connected components of directed graph g as lists of vertices.

WeightingFunction is an option to the functions SetEdgeWeights and SetVertexWeights that tells the functions how to compute edge weights and vertex weights, respectively.