VertexAdd
VertexAdd[g, v] makes a graph by adding the vertex v to the graph g.
VertexAdd[g, {v1, v2, ...}]adds a collection of vertices to g.VertexAdd[{v -> w, ...}, ...]uses rules v -> w to specify the graph g.
Examples
VertexAdd[Graph[{1 -> 2, 2 -> 3}], 4]VertexAdd[CycleGraph[4], {5, 6}]Please visit the official Wolfram Language Reference for more details.