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

<Previous Article In Volume
Next Article In Volume>

On Rainbow Antimagic Coloring of Some Classes of Graphs

Authors
Indah Lutfiyatul Mursyidah1, Dafik1, 2, Arika Indah Kristiana1, 2, Ika Hesti Agustin2, 3, *, Ika Nur Maylisa2, Ridho Alfarisi2, 4
1Department of Postgraduate Mathematics Education, University of Jember, Jember, Indonesia
2PUI-PT Combinatorics and Graph, CGANT, University of Jember, Jember, Indonesia
3Department of Mathematics, University of Jember, Jember, Indonesia
4Department of Elementary School, University of Jember, Jember, Indonesia
*Corresponding author. Email: ikahesti.fmipa@unej.ac.id
Corresponding Author
Ika Hesti Agustin
Available Online 27 April 2023.
DOI
10.2991/978-94-6463-138-8_8How to use a DOI?
Keywords
Edge coloring; rainbow antimagic coloring; vertex amalgamation
Abstract

This study aims to develop rainbow antimagic coloring. A graph G is said to be a rainbow antimagic coloring if there is a bijection function f : V ( G ) → { 1 , 2 , . . . , V ( G ) } , and the associated weight of an edge u v ∈ E ( G ) under f is w f ( u v ) = f ( u ) + f ( v ) . If there is w f ( u v ) ≠ w f ( u ′ v ′ ) for every two edges u v , u ′ v ′ in E(P), a path P in a vertex-labeled graph G is said to be a rainbow path. The purpose of this paper is to study the rainbow antimagic coloring and determine the smallest number of rainbow antimagic connection number, denoted by rac(G), where G is the vertex amalgamation of some graphs, namely fan graph F p , dragon graph D g p , bow graph B p , q , and wheel graph W p . In this paper, we complete previous research of rainbow antimagic connection number of vertex amalgamation product of fan graph until reaching the lower bound.

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.

Download article (PDF)

<Previous Article In Volume
Next Article In Volume>
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_8
ISSN
2352-541X
DOI
10.2991/978-94-6463-138-8_8How 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  - Indah Lutfiyatul Mursyidah
AU  - Dafik
AU  - Arika Indah Kristiana
AU  - Ika Hesti Agustin
AU  - Ika Nur Maylisa
AU  - Ridho Alfarisi
PY  - 2023
DA  - 2023/04/27
TI  - On Rainbow Antimagic Coloring of Some Classes of Graphs
BT  - Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)
PB  - Atlantis Press
SP  - 73
EP  - 93
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-138-8_8
DO  - 10.2991/978-94-6463-138-8_8
ID  - Mursyidah2023
ER  -