On rainbow antimagic coloring of special graphs

• Published in: Journal of physics. Conference series Vol. 1836; no. 1; p. 12016
• Main Authors: Septory, B J, Utoyo, M I, Dafik, Sulistiyono, B, Agustin, I H
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.03.2021
• Subjects: Coloring; Double stars; Graph theory; Labeling; Physics; Vertex sets
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1836/1/012016

Abstract Let G(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 and u’v’ in path x — y,w(uv) = w(u’v ’) w(uv), where w(uv) = f (u) + f (v) and x,y ∈ V(G). A graph G is a rainbow antimagic connection if G has a rainbow antimagic labeling. Thus any rainbow antimagic labeling induces a rainbow coloring of G where the edge uv is assigned with the color w(uv). The rainbow antimagic connection number of G, denoted by rac(G), is the smallest number of colors taken over all rainbow colorings induced by rainbow antimagic labeling of G . In this paper, we show the exact value of the rainbow antimagic connection number of jahangir graph J 2 , m , lemon graph Le m , firecracker graph (F m , 3), complete bipartite graph (K 2 , m ), and double star graph (S m , m ).