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

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On Rainbow Vertex Antimagic Coloring of Shell Related Graphs

Authors
Agnes Ayu Utami Ulya Kamila1, Dafik2, *, Arika Indah Kristiana1, 2, Rosanita Nisviasari2, Elsa Yuli Kurniawati2
1Department of Postgraduate Mathematics Education, 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 27 April 2023.
DOI
10.2991/978-94-6463-138-8_3How to use a DOI?
Keywords
rainbow vertex coloring; rainbow vertex antimagic coloring; shell graph
Abstract

A rainbow vertex antimagic coloring namely rainbow vertex coloring and antimagic labeling. For a bijective function f E ( G ) → 1 , 2 , 3 ⋯ , E G , the associate weight of a vertex v ϵ V G against f is W f v = ∑ e ϵ E v f e , where E(v) is the set of vertices incident to v. The function f is known as vertex antimagic labeling if every vertex has a distinct weight. Any path P in a graph G labeled with edges called a rainbow path if any two interior vertices on the path u - v have different weights. If there is a rainbow path u - v between every pair of u and v vertices, then f is referred to as the rainbow vertex antimagic labeling of G. Graph G is called rainbow vertex antimagic coloring when each u - v edge has a vertex weight color wf(v). The deductive analytic method is used in this research to analyze the issues that have been discovered, define the issue, and demonstrate patterns and theorems. With n ranging, the steps required are to draw a graph, determine the cardinality, search for the pattern of the rainbow vertex connection number as the lower bound, construct the bijective function to obtain the upper bound, and if the upper bound meets the lower bound, than new theorems and their proofs will be generated. Using the results of the proven theorem analysis will form a conclusion. BF(n, m) and shell flower graph [ C n , n - 3 , k 2 ] k

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_3
ISSN
2352-541X
DOI
10.2991/978-94-6463-138-8_3How 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  - Agnes Ayu Utami Ulya Kamila
AU  - Dafik
AU  - Arika Indah Kristiana
AU  - Rosanita Nisviasari
AU  - Elsa Yuli Kurniawati
PY  - 2023
DA  - 2023/04/27
TI  - On Rainbow Vertex Antimagic Coloring of Shell Related Graphs
BT  - Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)
PB  - Atlantis Press
SP  - 17
EP  - 29
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-138-8_3
DO  - 10.2991/978-94-6463-138-8_3
ID  - Kamila2023
ER  -