The translation of graphs is explored A translation is a movement of the graph either horizontally parallel to the x -axis or vertically parallel to the y -axis.

Hyungryul Baik, Hyunshik Shin, Chenxi Wu, An Upper Bound on the Asymptotic Translation Lengths on the Curve Graph and Fibered Faces, Indiana University Mathematics Journal, Vol. 70, No. 4 (2021), pp.