VertexNumberPosition is an option that can be used in ShowGraph to display a vertex number in a certain position relative to the vertex.
VertexStyle is an option that allows the user to associate different sizes and shapes to vertices.
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Convert To opens a submenu for converting a cell to another form, format, or display form.
Compiled is an option for various numerical and plotting functions which specifies whether the expressions they work with should automatically be compiled.
EdgeAdd
(Built-in Mathematica Symbol) EdgeAdd[g, e] makes a graph by adding the edge e to the graph g.EdgeAdd[g, {e_1, e_2, ...}] adds a collection of edges to g.
RemoveProperty[{obj, item}] removes all properties associated with item in obj.RemoveProperty[{obj, item}, name] removes the property name associated with item in obj.
VertexAdd[g, v] makes a graph by adding the vertex v to the graph g.VertexAdd[g, {v_1, v_2, ...}] adds a collection of vertices to g.