Definition:Subdivision (Graph Theory)

Edge subdivision operation
Let $G = (V, E)$ be a graph.

The edge subdivision operation for an edge $\{u, v\} \in E$ is the deletion of $\{u, v\}$ from $G$ and the addition of two edges $\{u, w\}$ and $\{w, v\}$, where $w \not \in V$.

Graph subdivision
Any graph derived from a graph $G$ by a sequence of edge subdivision operations is called a subdivision of $G$ or a $G$-subdivision.

Example
This:


 * Example_subdivision_graph.png

is a subdivision of this:


 * ExampleOfGraph.png

by splitting edges $\{A, E\}$ and $\{C, D\}$.