The R-dynamic local irregularity vertex coloring of graph

We define the r-dynamic local irregularity vertex coloring. Suppose λ: V(G) → {1,2, …, k} is called vertex irregular k-labeling and w: V(G) → N where (formula presented). λ is called r-dynamic local irregular vertex coloring, if: (i) opt(λ) = min{max{λi}; λ_i vertex irregular k-labeling}, (ii) for every uv Є E(G), w(u) ≠ w(v), and (iii) for every v Є V(G) such that |w(N(v))| ≥ min{r, d(v)}. The chromatic number r-dynamic local irregular denoted by (formula presented), is minimum of cardinality r-dynamic local irregular vertex coloring. We study the r-dynamic local irregularity vertex coloring of graph and we have found the exact value of chromatic number r-dynamic local irregularity of some graph.