User:Scshunt/Definition:Incidence Function of Graph

Definition

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

Then the incidence function of $G$ is the function $\phi : V \times E \to \set {0, 1}$ defined by:

$\map \phi {v, e} = 1$ if and only if $v$ is incident to $e$.

That is:

$\map \phi {v, e} = \begin{cases} 1 &: v \in e \\ 0 &: v \notin e \end{cases}$

Note that $\phi$ is a graph incidence function.