A graceful k-coloring of a non-empty graph G = (V, E) is a proper vertex coloring f : V (G) → {1, 2, ..., k}, k ≥ 2, which induces a proper edge coloring f*: E(G) → {1, 2, ..., k − 1} defined by f*(uv) = |f(u) − f(v)|, ...