Definition:Subdivision (Graph Theory)/Edge

Definition
Let $G = \struct {V, E}$ be a graph.

The edge subdivision operation for an edge $\set {u, v} \in E$ is the deletion of $\set {u, v}$ from $G$ and the addition of two edges $\set {u, w}$ and $\set {w, v}$ along with the new vertex $w$.

This operation generates a new graph $H$:
 * $H = \struct {V \cup \set w, \paren {E \setminus \set {u, v} } \cup \set {\set {u, w}, \set {w, v} } }$

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

Also see

 * Definition:Graph Subdivision: a graph obtained from another by a sequence of edge subdivisions.