Sharp lower bounds on the metric dimension of circulant graphs

For $n ge 2t+1$ where $t ge 1$, the circulant graph $C_n (1, 2, dots , t)$ consists of the vertices $v_0, v_1, v_2, dots , v_{n-1}$ and the edges $v_i v_{i+1}$, $v_i v_{i+2}, dots , v_i v_{i + t}$, where $i = 0, 1, 2, dots , n-1$, and the subscripts are taken modulo $n$. We prove that the metric dimension ${rm dim} (C_n (1, 2, dots , t)) ge leftlceil frac{2t}{3} rightrceil + 1$ for $t ge 5$, where the equality holds if and only if $t = 5$ and $n = 13$. Thus ${rm dim} (C_n (1, 2, dots , t)) ge leftlceil frac{2t}{3} rightrceil + 2$ for $t ge 6$. This bound is sharp for every $t ge 6$.