Every now and then I wonder what the official name of the relation $\sim$ between two vertices in a graph $G$ is that are mapped to each other by a graph automorphism, i.e. which are "structurally indistinguishable":

$$x \sim y \quad\text{iff}\quad (\exists g \in \text{Aut}(G))\ x = g(y)$$

I use to call such vertices "conjugate", more cumbersome is "in the same orbit". Rudolf Carnap in *Logical Structure of the world* uses the term "homotopic" and I dimly remember to have heard the term "homologous".

None of these terms gives many relevant Google results when combined with "graph theory" (but maybe I just searched awkwardly?). But this could also mean, that the concept per se isn't of very big interest in graph theory?