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)vertical bar g is called a local antimagic labeling if for all uv is an element of E(G)s, w(u) not equal w(v), where w(u) = Sigma(e is an element of 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 chi(r)la (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.