Reference question for a generalization of vertex coloring

Question

I am wondering whether there is a standard convention for the following generalization of the vertex coloring.

An $n$-diameter coloring is a vertex coloring such that vertices between which there exists a path of length $\leq n$ have distinct colors. So the usual coloring would be $1$-diameter coloring.

Answer 1

It's usually called a distance colouring.

See the survey by Kramer and Karmer,

https://www.sciencedirect.com/science/article/pii/S0012365X0700386X#:~:text=A%20distance%2Dcolouring%20relative%20to,than%20p%20have%20distinct%20colours.