Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)

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A Study of the Rainbow Antimagic Coloring of Double Wheel and Parachute Graphs

Authors
Syahril Maghfiro1, Dafik2, 3, *, Arika Indah Kristiana2, 3, Rosanita Nisviasari2, Slamin2, 4, Ika Hesti Agustin2, 5
1Postgraduate Mathematics Education Program, University of Jember, Jember, Indonesia
2PUI-PT Combinatorics and Graph, CGANT, University of Jember, Jember, Indonesia
3Mathematics Education Department, University of Jember, Jember, Indonesia
4Information Systems Department, University of Jember, Jember, Indonesia
5Mathematics Department, University of Jember, Jember, Indonesia
*Corresponding author.
Corresponding Author
Dafik
Available Online 27 April 2023.
DOI
10.2991/978-94-6463-138-8_11How to use a DOI?
Keywords
rainbow antimagic connection number; double wheel graph; parachute graph; rainbow connection number
Abstract

In this study, we explore the idea of rainbow antimagic coloring, which combines the notions of antimagic labeling with rainbow coloring. We consider a connected and simple graph G(V, E) with a vertex set V(G) and an edge set E(G). A vertex labeling of graph G is defined as a bijective function f : V ( G ) → { 1 , 2 , 3 , . . . , k } , where the resulting weight for an edge u v ∈ E ( G ) is determined by the function f ( u ) + f ( v ) = w f ( u v ) . A set of edge weight functions (W(G)) is obtained from the edge weight function (wf(uv)), and is determined by the cardinality of the set (|W(G)|). A function f of graph G is considered a rainbow antimagic labeling if the weight of any two edges uv and u ′ v ′ on the path u - v are distinct. The minimum amount of hues necessary for a rainbow coloring that emerges from a rainbow antimagic labeling of graph G, denoted as rac(G), is referred to as the rainbow antimagic connection number. Our study has led to the discovery of the precise numerical values for rac(G) of both a double wheel graph and a parachute graph. Specifically, r a c ( D W n ) = 2 n and r a c ( P C n ) = n + 2 .

Copyright
© 2023 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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Volume Title
Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)
Series
Advances in Physics Research
Publication Date
27 April 2023
ISBN
10.2991/978-94-6463-138-8_11
ISSN
2352-541X
DOI
10.2991/978-94-6463-138-8_11How to use a DOI?
Copyright
© 2023 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.

Cite this article

risenwbib
TY  - CONF
AU  - Syahril Maghfiro
AU  - Dafik
AU  - Arika Indah Kristiana
AU  - Rosanita Nisviasari
AU  - Slamin
AU  - Ika Hesti Agustin
PY  - 2023
DA  - 2023/04/27
TI  - A Study of the Rainbow Antimagic Coloring of Double Wheel and Parachute Graphs
BT  - Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)
PB  - Atlantis Press
SP  - 120
EP  - 132
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-138-8_11
DO  - 10.2991/978-94-6463-138-8_11
ID  - Maghfiro2023
ER  -