An r-dynamic coloring of a graph G is a proper coloring of G such that every vertex in V(G) has neighbors in at least $\min\{d(v),r\}$ different color classes. The r-dynamic chromatic number of graph G denoted as $\chi_r (G)$, is the least k such that G has a coloring. In this paper we obtain the r-dynamic chromatic number of the central graph, middle graph, total graph, line graph, para-line graph and sub-division graph of the comb graph $P_n\odot K_1$ denoted by $C(P_n\odot K_1), M(P_n\odot K_1), T(P_n\odot K_1), L(P_n\odot K_1), P(P_n\odot K_1)$ and $S(P_n\odot K_1)$ respectively by finding the upper bound and lower bound for the r-dynamic chromatic number of the Comb graph.

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Let G = (V, E) be a simple finite connected and undirected graph with n vertices and m edges. The n vertices are assigned the colors through mapping c : V [G] → I +. An r-dynamic coloring is a proper k-coloring of a graph G such that each vertex of G receive colors in at least min{deg(υ),r} different color classes. The minimum k such that the graph G has r-dynamic k coloring is called the r-dynamic chromatic number of graph G denoted as χ r (G). Let G 1 and G 2 be a graphs with n 1 and n 2 vertices and m 1 and m 2 edges. The central vertex join of G1 and G 2 is the graph G 1   V ˙   G 2 is obtained from C(G 1) and G 2 joining each vertex of G 1 with every vertex of G 2. The aim of this paper is to obtain the lower bound for r-dynamic chromatic number of central vertex join of path with a graph G, central vertex join of cycle with a graph G and r-dynamic chromatic number of P m V ˙   P n ,   P m V ˙   K n ,   P m V ˙   K n ,   P m V ˙   C n ,   C m V ˙   K n and C m V ˙   C n respectively.