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

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On Local (a, d)-Edge Antimagic Coloring of Some Graphs

Authors
Rifda Izza1, Dafik1, 2, Arika Indah Kristiana1, 2, Ika Hesti Agustin2, 3, *, Ika Nur Maylisa2, Elsa Yuli Kurniawati2
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
*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_4How to use a DOI?
Keywords
local (a;  d) antimagic coloring; edge antimagic coloring; spacial graph
Abstract

All graphs considered in this paper are simple, finite and connected graph. Let G(V, E) be a graph with the vertex set V and the edge set E, and let w be the edge weight of graph G. with | V ( G ) | = m and | E ( G ) | = n . A labeling of a graph G is a bijection f from V(G) to the set { 1 , 2 , . . . , | V ( G ) | } . The bijection f is called an edge antimagic labeling of graph if for any two vertex u and v in path x - y , u ≠ v , where { w ( u v ) : w ( u v ) = f ( u ) + f ( v ) , u v ∈ E } , are distinct. Any local edge antimagic labeling induces a proper edge coloring of G where the edge uv is assigned the color w(uv). The local edge antimagic coloring of graph is said to be a local (a, d)-edge antimagic coloring of G if the set of their edge colors form an arithmetic sequence with initial value a and different d. The local (a, d)-edge antimagic chromatic number χ la ( a , d ) ( G ) is the minimum number of colors needed to color G such that a graph G admits the local (a, d)-edge antimagic coloring. Furthermore, In this paper, we will obtain the lower and upper bound of χ la ( a , d ) ( G ) . The results of this research are the exact value of the local (a, d)-edge antimagic chromatic number of some graphs.

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
978-94-6463-138-8
ISSN
2352-541X
DOI
10.2991/978-94-6463-138-8_4How 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  - Rifda Izza
AU  - Dafik
AU  - Arika Indah Kristiana
AU  - Ika Hesti Agustin
AU  - Ika Nur Maylisa
AU  - Elsa Yuli Kurniawati
PY  - 2023
DA  - 2023/04/27
TI  - On Local (a, d)-Edge Antimagic Coloring of Some Graphs
BT  - Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)
PB  - Atlantis Press
SP  - 30
EP  - 41
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-138-8_4
DO  - 10.2991/978-94-6463-138-8_4
ID  - Izza2023
ER  -