Definition:Complement (Graph Theory)/Simple Graph

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Definition

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

The complement of $G$ is the simple graph $\overline G = \struct {V, \overline E}$ which consists of:

The same vertex set $V$ of $G$
The set $\overline E$ defined such that $\set {u, v} \in \overline E \iff \set {u, v} \notin E$, where $u$ and $v$ are distinct.


Linguistic Note

The word complement comes from the idea of complete-ment, it being the thing needed to complete something else.

It is a common mistake to confuse the words complement and compliment.

Usually the latter is mistakenly used when the former is meant.