On rainbow antimagic coloring of special graphs
Brian Juned Septory, Mohammad Imam Utoyo, Dafik Dafik, B Sulistiyono, Ika Hesti Agustin · Journal of Physics Conference Series · 2021
Abstract LetG(V, E)be a connected, undirected and simple graph with vertex set V(G) and edge set E(G). A labeling of a graph G is a bijection f from V(G) to the set {1, 2,…, | V(G)|}. The bijection f is called rainbow antimagic vertex labeling if for any two edge uv andu’v’in pathx — y,w(uv)=w(u’v’)w(uv),wherew(uv)= f (u) + f (v) andx,y ∈V(G). A graph G is a rainbow antimagic connection ifGhas a rainbow antimagic labeling. Thus any rainbow antimagic labeling induces a rainbow coloring ofGwhere the edgeuvis assigned with the color w(uv). The rainbow antimagic connection number of G, denoted byrac(G),is the smallest number of colors taken over all rainbow colorings induced by rainbow antimagic labeling ofG. In this paper, we show the exact value of the rainbow antimagic connection number of jahangir graph J2,m, lemon graphLem,firecracker graph(Fm,3), complete bipartite graph (K2,m), and double star graph (Sm,m).