Uniquely colorable graph

A uniquely colorable graph is a type of graph where you can use different colors to color each piece (called a vertex) so that no two pieces that are connected to each other have the same color. Imagine the graph looks like a bunch of dots connected by lines. You can pick different colors (such as red, blue, green, etc.) to color each dot, but no dots that are connected to one another can be the same color.