Defining numbers in some of the Harary graphs

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 ≥ χ ( 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. In this note, we study the chromatic number, the defining number and the strong defining number in some of the Harary graphs.