Definition:Graph (Graph Theory)/Vertex
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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
A vertex of a graph $G$, particularly when $G$ is a tree, is also known as a node.
Also see
- 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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): graph: 2.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): vertex: 2. (plural vertices)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): graph: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): vertex: 2. (plural vertices)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): vertex (of a graph)