On Rainbow Antimagic Coloring of Graphs

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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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  -