Proceedings of the 2nd International Conference on Neural Networks and Machine Learning 2023 (ICNNML 2023)

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On Rainbow Antimagic Coloring of Graphs

Authors
M. I. N. Annadhifi1, Dafik1, 2, *, A. I. Kristiana1, 2, E. Y. Kurniawati2, R. Nisviasari2, E. S. W. Jannah1, 2
1Department of Mathematics Edu. Post Grad., University of Jember, Jember, Indonesia
2PUI-PT Combinatorics and Graph, CGANT, University of Jember, Jember, Indonesia
*Corresponding author. Email: d.dafik@unej.ac.id
Corresponding Author
Dafik
Available Online 29 June 2024.
DOI
10.2991/978-94-6463-445-7_16How to use a DOI?
Keywords
rainbow antimagic coloring; rainbow antimagic connection number; graph coloring
Abstract

Let G be a simple graph. For a bijective function f : V ( G ) → { 1 , 2 , . . . , | V ( G ) | } , the edge weight for any u v ∈ E ( G ) under f is w f ( u v ) = f ( u ) + f ( v ) . A path P in a graph G is said to be a rainbow path, if for every two edges uv, u ′ v ′ ∈ E ( P ) , the edges weight satisfies w f ( u v ) ≠ w f ( u ′ v ′ ) . If for every two vertices u and v of G, there exists a rainbow path u-v, then f is called a rainbow antimagic coloring of graph G. The minimum number of colors induced by all edge weight required is called rainbow antimagic connection number, denoted by (rac(G)). In this research, we will find the rainbow antimagic connection number rac(G) and new theorems on rainbow antimagic coloring of Double Quadrilateral Windmill Graph D Q ( n ) , Double Quadrilateral Flower Graph F D Q ( m ) , Split Graph of Star S p l ( K 1 , n ) and Tunjung Graph T j n .

Copyright
© 2024 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 2nd International Conference on Neural Networks and Machine Learning 2023 (ICNNML 2023)
Series
Advances in Intelligent Systems Research
Publication Date
29 June 2024
ISBN
978-94-6463-445-7
ISSN
1951-6851
DOI
10.2991/978-94-6463-445-7_16How to use a DOI?
Copyright
© 2024 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  - M. I. N. Annadhifi
AU  - Dafik
AU  - A. I. Kristiana
AU  - E. Y. Kurniawati
AU  - R. Nisviasari
AU  - E. S. W. Jannah
PY  - 2024
DA  - 2024/06/29
TI  - On Rainbow Antimagic Coloring of Graphs
BT  - Proceedings of the 2nd International Conference on Neural Networks and Machine Learning 2023 (ICNNML 2023)
PB  - Atlantis Press
SP  - 155
EP  - 165
SN  - 1951-6851
UR  - https://doi.org/10.2991/978-94-6463-445-7_16
DO  - 10.2991/978-94-6463-445-7_16
ID  - Annadhifi2024
ER  -