An r-dynamic proper k-coloring of a graph G is a proper k-coloring of G such that every vertex in V (G) has neighbors in atleast min {r, d(v)} different color classes. The r-dynamic chromatic number of a graph G is the minimum k such that G has an r-dynamic coloring with k colors. In this paper we investigate the r-dynamic chromatic number for the Central graph, Middle graph, Total graph and Line graph of Double star graph. © Palestine Polytechnic University-PPU 2021.