The mixed metric dimension of flower snarks and wheels

Abstract

New graph invariant, which is called mixed metric dimension, has been recently introduced. In this paper, exact results of mixed metric dimension on two special classes of graphs are found: flower snarks $J_n$ and wheels $W_n$. It is proved that mixed metric dimension for $J_5$ is equal to 5, while for higher dimensions it is constant and equal to 4. For $W_n$, its mixed metric dimension is not constant, but it is equal to $n$ when $n\geq 4$, while it is equal to 4, for $n=3$.