Local antimagic r-dynamic coloring of graphs

Let G = (V, E) be a connected graph. A bijection function f : E(G) → {1,2, 3, • • •, E(G)|} is called a local antimagic labeling if for all uv ∈ E(G)s, w(u) ≠ w(v), where w(u) = ∑_e∈E(u) f(e). Such that, local antimagic labeling induces a proper vertex k-coloring of graph G that the neighbors of any vertex u receive at least min{r, d(v)} different colors. The local antimagic r-dynamic chromatic number, denoted by (G) is the minimum k such that graph G has the local antimagic r-dynamic vertex k-coloring. In this paper, we will present the basic results namely the upper bound of the local antimagic r-dynamic chromatic number of some classes graph.