In a given graph G=(V,E), a set of vertices S with an assignment of colors to them is said to be a defining set of the vertex coloring of G if there exists a unique extension of the colors of S to a c < chi(G) coloring of the vertices of G. A defining set with minimum cardinality is called a minimum defining set and its cardinality is the defining number, denoted by d(G, c ). The defining set S is strong, if there exist an ordering {v_1,v_2, \dots, v_{n-s}} of
