On the rainbow antimagic coloring of vertex amalgamation of graphs

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 mi...

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Bibliographic Details
Published in:Journal of physics. Conference series 2022-01, Vol.2157 (1), p.12014
Main Authors: Joedo, J C, Dafik, Kristiana, A I, Agustin, I H, Nisviasari, R
Format: Article
Language:English
Subjects:
Amalgamation
Apexes
Coloring
Graph theory
Graphs
Labels
Physics
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Summary: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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/2157/1/012014