THE DISTANCE CHROMATIC NUMBER OF SPECIAL GRAPHS

The distance power G(d) of a graph G has the same vertex set as G. Distinct vertices in G(d) are adjacent, if their distance in G is at most d. For positive integers q; n the graph Gq;n has as its vertex set the n-fold Cartesian product Zq £ ¢ ¢ ¢ £ Zq;Zq = f0; 1; :::; q ¡ 1g: Vertices in Gq;n are adjacent, if they differ in exactly one coordinate. In this paper, some exact values of Â(G(d) q;n) have been determined and for fixed d and n, Â(G(d) q;n) = qd + O(qd¡1).