Sharp lower bounds on the metric dimension of circulant graphs

For n >= 2t + 1 where t >= 1, the circulant graph C-n(1, 2, ... , t) consists of the vertices v(0), v(1), v(2), ... , v(n-1) and the edges v(i)v(i+1), v(i)v(i+2), ... , v(i)v(i+t), where i = 0, 1, 2, ... , n - 1, and the subscripts are taken modulo n. We prove that the metric dimension dim(C-n(1, 2, ... , t)) >= inverted right perpendicular2t/3inverted left perpendicular + 1 for t >= 5, where the equality holds if and only if t = 5 and n = 13. Thus dim(C-n(1, 2, ... , t)) >= inverted right perpendicular2t/3inverted left perpendicular + 2 for t >= 6. This bound 3 is sharp for every t >= 6.