Definition:Graph of Mapping

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This page is about Graph in the context of Mapping Theory. For other uses, see Graph.


Let $S$ and $T$ be sets.

Let $f: S \to T$ be a mapping.

The graph of $f$ is the relation $\RR \subseteq S \times T$ defined as $\RR = \set {\tuple {x, \map f x}: x \in S}$

Alternatively, this can be expressed:

$G_f = \set {\tuple {s, t} \in S \times T: \map f s = t}$

where $G_f$ is the graph of $f$.

The word is usually used in the context of a diagram:


Graph of a Relation

The concept can still be applied when $f$ is a relation, but in this case a vertical line through a point in the graph is not guaranteed to intersect the graph at one and only one point.

Also denoted as

The symbol $\Gamma_f$ is sometimes seen to denote the graph of $f$.


Graph of Mapping/Examples

Also see

  • Results about Graphs of Mappings can be found here.