A graph with such a coloring is called a vertex-colored graph.
- Definition:Labeled Graph: a vertex-colored graph can be considered as a labeled graph in which the labels are considered as colors.
- Definition:Proper Coloring, in which adjacent vertices or edges are required to have different colors.
The British English spelling of color and coloring is colour and colouring.
They are traditionally referred to as colors because this subfield of graph theory arose from considerations of the coloring of the faces of planar graphs such that adjacent faces have different colors.
This was the origin of the famous Four Color Theorem.