TY - JOUR

T1 - On rainbow antimagic coloring of special graphs

AU - Septory, B. J.

AU - Utoyo, M. I.

AU - Dafik,

AU - Sulistiyono, B.

AU - Agustin, I. H.

N1 - Publisher Copyright:
© 2021 Published under licence by IOP Publishing Ltd.

PY - 2021/3/23

Y1 - 2021/3/23

N2 - 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 J2,m, lemon graph Lem, firecracker graph (Fm,3), complete bipartite graph (K2,m), and double star graph (Sm,m).

AB - 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 J2,m, lemon graph Lem, firecracker graph (Fm,3), complete bipartite graph (K2,m), and double star graph (Sm,m).

UR - http://www.scopus.com/inward/record.url?scp=85103568528&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1836/1/012016

DO - 10.1088/1742-6596/1836/1/012016

M3 - Conference article

AN - SCOPUS:85103568528

SN - 1742-6588

VL - 1836

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012016

T2 - 4th International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2020

Y2 - 22 August 2020 through 23 August 2020

ER -