Edge and mixed metric dimension of Johnson graphs

In this paper, both edge and mixed metric dimensions of Johnson graphs $J_{n,k}$ are considered. A new tight lower bound for ${\beta }_E(J_{n,k})$ based on hitting sets has been obtained. Using this bound, exact values for ${\beta }_E(J_{n,2})$ and ${\beta }_M(J_{n,2})$ have been derived, and it is proved that ${\beta }_E(J_{n,2})={\beta }_M(J_{n,2})$.