VertexCoordinates is an option to Graph and related functions that specifies the coordinates to use to place the center of vertices.
VertexCount[g] gives a count of the number of vertices in the graph g.VertexCount[g, patt] gives a count of the number of vertices that match the pattern patt.
VertexCoverQ[g, vlist] yields True if the vertex list vlist is a vertex cover of the graph g, and False otherwise.
VertexDegree[g] gives the list of vertex degrees for all vertices in the graph g.VertexDegree[g, v] gives the vertex degree for the vertex v.
VertexDelete[g, v] makes a graph by deleting the vertex \[Nu] and all edges connected to v from the graph g.VertexDelete[g, {v_1, v_2, ...}] deletes a collection of vertices ...
VertexEccentricity[g, s] gives the length of the longest shortest path from the source s to every other vertex in the graph g.
VertexInComponent[g, {v_1, v_2, ...}] gives the vertices in the graph g that have a directed path to at least one of v_1, v_2, ....VertexInComponent[g, {v_1, v_2, ...}, k] ...
VertexInDegree[g] gives the list of vertex in-degrees for all vertices in the graph g.VertexInDegree[g, v] gives the vertex in-degree for the vertex v.
VertexIndex[g, v] gives the integer index for the vertex v in the graph g.
VertexLabeling is an option for GraphPlot and related functions which specifies whether labeling should be included by default for vertices in graphs.