Definition:Edge Deletion

Definition

Let $G = \struct {V, E}$ be an (undirected) graph.

Let $F \subseteq E$ be a set of edges of $G$.

Then the graph obtained by deleting $F$ from $G$, denoted by $G \setminus F$, is the subgraph of $G$ containing the same vertices as $G$ but with all the elements of $F$ removed.

That is:

$G \setminus F = \struct {V, E \setminus F}$

Informally, $G \setminus F$ is the graph obtained from $G$ by removing all edges in $F$.

Also denoted as

The edge deletion $G \setminus F$ can also be denoted as $G - F$

If $F$ is a singleton such that $F = \set e$, then $G \setminus F$ may be expressed $G \setminus e$.

Also see

• Definition:Vertex Deletion

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): $\S 2.4$: Cut-Vertices and Bridges