Definition:Graph (Graph Theory)/Vertex

Definition

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 $e$.

• Definition:Odd Vertex (Graph Theory)
• Definition:Even Vertex (Graph Theory)

• 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.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs
• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.2$ Graphs and Trees
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$)
• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The Bridges of Königsberg
• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 2.3.4.1$: Free Trees
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): vertex (of a graph)