Definition:Graph (Graph Theory)/Vertex

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

The vertices (singular: vertex) are the elements of $V$.

Informally, the vertices are the points that are connected by the edges.

In the above, the vertices are the points $A, B, C, D, E, F, G$ which are marked as dots.

Also known as

When $G$ is a tree, the vertices are usually called nodes.

Also see

If $e \in E$ is an edge joining the vertex $u$ to the vertex $v$, $u$ and $v$ are called the endvertices of $e$.

  • Results about vertices of graphs can be found here.

Linguistic Note

The plural of vertex is vertices.

The word vertex is Latin for peak, from which the irregular plural form.