Graph subdivision

A subdivision of a graph is created by adding new vertices along the existing edges of the graph.

This basically breaks the original edges into smaller segments, joined by the new vertices.

We cannot add any edges, or any vertices that are not on existing edges. We can only add vertices such that they split up existing edges.

Example

Consider this graph:

A ----- B
 \     /
   \ /  
    C

A subdivision of this graph could be:

A - D - B
 \     /
   \ /  
    C

As you can see, we added a new vertex D along the edge between A and B, splitting what was one edge (A-B) into two edges (A-D and D-B).

Question	Answer
Graph subdivision	Subdivision is created by adding new vertices along existing edges, breaking original edges into smaller segments. Cannot add edges or vertices not on existing edges.
What restriction exists when subdividing a graph?	We cannot add any edges, or any vertices that are not on existing edges. We can only add vertices such that they split up existing edges.
In the example graph A-B-C where edge A-B exists, what does adding vertex D along A-B do?	It splits edge A-B into two edges: A-D and D-B.