 Uniquely colorable graph

A uniquely colorable graph is a type of graph in graph theory that can be colored in such a way that there is only one valid coloring that satisfies a given set of constraints. Specifically, a graph is uniquely colorable if there is a proper vertex coloring (where no two adjacent vertices share the same color) that can be achieved using a specific set of colors, and there are no other configurations that yield a valid coloring with the same constraints.