Local Antimagic r-dynamic Coloring of Graphs

Abstract

Let G = (V; E) be a connected graph. A bijection function f : E(G) ! f1; 2; 3; ; E(G)jg is called a local antimagic labeling if for all uv 2 E(G)s, w(u) 6= w(v), where w(u) = e2E(u)f(e). Such that, local antimagic labeling induces a proper vertex kcoloring of graph G that the neighbors of any vertex u receive at least minfr; d(v)g di erent colors. The local antimagic r-dynamic chromatic number, denoted by la r (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.