Definition:Subdivision (Graph Theory)

Edge Subdivision
Let $G = \left({V, E}\right)$ be a graph.

The edge subdivision operation for an edge $\left\{{u, v}\right\} \in E$ is the deletion of $\left\{ {u, v}\right\}$ from $G$ and the addition of two edges $\left\{ {u, w}\right\}$ and $\left\{ {w, v}\right\}$, where $w \notin V$.

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 $\left\{ {A, E}\right\}$ and $\left\{ {C, D}\right\}$.