Open AccessOn the rainbow antimagic coloring of vertex amalgamation of graphs
Author(s) -
J C Joedo,
Dafik Dafik,
Arika Indah Kristiana,
Ika Hesti Agustin,
Rosanita Nisviasari
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2157/1/012014
Subject(s) - rainbow , combinatorics , mathematics , vertex (graph theory) , edge coloring , connection (principal bundle) , graph , path (computing) , discrete mathematics , graph power , computer science , line graph , physics , geometry , computer network , quantum mechanics
The purpose of this study is to develop rainbow antimagic coloring. This study is a combination of two notions, namely antimagic and rainbow concept. If every vertex of graph G is labeled with the antimagic labels and then edge weight of antimagic labels are used to assign a rainbow coloring. The minimum number of colors for a rainbow path to exist with the condition satisfying the edge weights w ( x ) ≠ w ( y ) for any two vertices x and y is the definition of the rainbow antimagic connection number rac ( G ). In this study, we use connected graphs and simple graphs in obtaining the rainbow antimagic connection number. This paper will explain the rainbow antimagic coloring on some graphs and get their formula of the rainbow antimagic connection number. We have obtained rac ( G ) where G is vertex amalgamation of graphs, namely path, star, broom, paw, fan, and triangular book graph.