Definition:Subdivision (Graph Theory)/Edge

Definition
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 $\left\{ {w, v}\right\}$ along with the new vertex $w$.

This operation generates a new graph $H$:
 * $H = \left({V \cup \left\{ {u} \right\}, \left({E \setminus \left\{{u, v}\right\} }\right) \cup \left\{ \left\{ {u, w}\right\}, \left\{ {w, v}\right\} \right\} }\right)$

Also known as
This operation is also known as elementary subdivision.

Also see
A graph obtained from another by a sequence of edge subdivisions is called a graph subdivision.