Definition:Boundary (Graph Theory)
This page is about the boundary of a vertex in the context of Graph Theory. For other uses, see Boundary.
other types of graph
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.
To discuss it in more detail, feel free to use the talk page.
If you are able to do this, then when you have done so you can remove this instance of {{Expand}} from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
Having done other types of graph, implement them as subpages and then transclude
Until this has been finished, please leave {{refactor}} in the code.
New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$.
Definition
Simple Graph
Let $G = \tuple {V, E}$ be a simple graph.
Let $v \in V$ be a vertex of $G$.
Then the boundary of $v$ is the set of all vertices of $G$ which are adjacent to $v$:
- $\map B v = \set {u \in V: \set {u, v} \in E}$
Source citations are highly desirable, and mandatory for all definition pages.
Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted.