Let c be a proper k-coloring of a connected graph G. Let Π = {S1, S2, . . . , Sk} be the induced partition of V (G) by c, where Si is the partition class having all vertices with color i. The color code cΠ(v) of vertex v is the ordered k-tuple (d(v, S1), d(v, S2), . . . , d(v, Sk)), where d(v, Si) = min{d(v, x)|x ∈ Si}, for 1 ≤ i ≤ k. If all vertices of G have distinct color codes, then c is ca...