On the r-dynamic chromatic number of subdivision of wheel graph

Let H be simple, non-isolated vertex, connected and directionless graphs with vertex set V (H), edge set E(H). With the use of c-coloring of graph H, using the formula c : υ(H) → S, where |S| = c, the colors of the adjacent vertex are different. A proper c-coloring of H is an r-dynamic coloring if it's applied to every vertex υ ∈ V (H) satisfies |c(N(υ))| ⩾ min {r, d(υ)}. The minimum c such that H has an r-dynamic coloring with c colors is called an r-dynamic chromatic number, denoted by χ_r (H). In this study, we will obtain the exact value of r-dynamic chromatic number of subdivision by wheel graph.