User:Scshunt/Definition:Incidence Function of Graph

Definition
Let $G = (V, E)$ be a graph.

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


 * $\phi\left({v, e}\right) = 1$ if and only if $v$ is incident to $e$.

That is:


 * $\phi\left({v, e}\right) = \begin{cases} 1 &: v \in e \\ 0 &: v \notin e \end{cases}$

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