ON THE METRIC DIMENSION OF CIRCULANT GRAPHS WITH 2 GENERATORS

A set of vertices W resolves a connected graph G if every vertex of G is uniquely determined by its vector of distances to the vertices in W. The number of vertices in a smallest resolving set is called the metric dimension and it is denoted by dim(G). We study the circulant graphs C-n (2, 3) with the vertices v(0), v(1), v(2), ... , v(n-1) and the edges v(i)v(i+2), v(i)v(i+3), where i = 0, 1, 2, ... , n - 1, the indices are taken modulo n. We show that for n >= 26 we have dim(C-n (2, 3)) = 3 if n equivalent to 4 (mod 6), dim(C-n (2, 3)) = 4 if n equivalent to 0, 1, 5 (mod 6) and 3 <= dim(C-n (2, 3)) <= 4 if n equivalent to 2, 3 (mod 6).