Rainbow Antimagic Coloring on Amalgamation of Wheel Graph (W₃)

DOI

10.2991/978-2-38476-410-5_9How to use a DOI?

Keywords

rainbow antimagic coloring; amalgamation; wheel graph

Abstract

Suppose G a simple, and finite graph. A labelling of a graph G is a bijection f from V(G) to the set {1,2,…,|V(G)|}. Rainbow antimagic coloring is a bijection f if for any two edge u and v in path u − v, where w(uv) = f(u) + f(v) and u,v ∈ V(G) and if in each pair of vertices u and v there are no two vertices that have the same weight in one path. A graph is said to be 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 colourings induced by rainbow antimagic labelling of G. We have found the bound of the rainbow antimagic connection graph with amalgamation operation of wheel graph (W₃), 3t ≤ rac(amal(W₃,v,t)) ≤ 3t + 2.

Copyright

© 2025 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Nisky Imansyah Yahya
AU  - Lailany Yahya
AU  - Cindra Dewi Husin
AU  - Sri Agista Kaya
AU  - Sulastri Akuba
AU  - Apon Ismail
PY  - 2025
DA  - 2025/07/28
TI  - Rainbow Antimagic Coloring on Amalgamation of Wheel Graph (W₃)
BT  - Proceedings of the 2nd International Conference on Sciences, Mathematics, and Education 2023 (ICOSMED 2023)
PB  - Atlantis Press
SP  - 91
EP  - 98
SN  - 2352-5398
UR  - https://doi.org/10.2991/978-2-38476-410-5_9
DO  - 10.2991/978-2-38476-410-5_9
ID  - Yahya2025
ER  -