Aut$(X) = \{\sigma \mid X^\sigma = X\}$, where $\sigma : X \mapsto X$ is a bijective map.
I am not getting the meaning of " Aut$(X)$- invariant vertex colouring".
I know the meaning of invariant means that does not change. So did it mean that suppose vertices of graph $X$ are colored than if we consider the group action of Aut$(X)$ on the vertices set of $X$ then it will preserve the color?
Motivation : I encounter this term while reading the some research paper related to graph and hyper-graph isomorphism.